Question 1

Multiply: $\sqrt [ 4 ] { 6 } \cdot \sqrt [ 8 ] { 6 }$

Accepted Answer

The answer of Multiply: \(\sqrt [ 4 ] { 6...

Question 2

Square both sides of the equation.  x+3+2=x−1\sqrt { x + 3 } + 2 = \sqrt { x - 1 }x+3​+2=x−1​

Accepted Answer

A)    x+5=x−1x + 5 = x - 1x+5=x−1 
B)    x+7=x−1x + 7 = x - 1x+7=x−1 
C)    x+2x+3+7=x−1x + 2 \sqrt { x + 3 } + 7 = x - 1x+2x+3c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​+7=x−1 
D)    x+4x+3+7=x−1x + 4 \sqrt { x + 3 } + 7 = x - 1x+4x+3c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​+7=x−1

Question 3

Multiply and simplify, if possible. $8 \sqrt { m n ^ { 3 } } ( 5 \sqrt { m n } )$

Accepted Answer

The answer of Multiply and simplify, if possible. \(8 \sqrt...

Question 4

In the expression  27x63\sqrt [ 3 ] { 27 x ^ { 6 } }327x6​  , the index is 3 and  27x627 x ^ { 6 }27x6  is the __________.

Accepted Answer

A)   power
B)   base
C)   radicand
D)   index
E)   argument

Question 5

Find  f(−4) f ( - 4 ) f(−4)   , given  f(x) =x−233f ( x )  = \sqrt [ 3 ] { x - 23 }f(x) =3x−23​

Accepted Answer

A)   3
B)   -3
C)   2
D)   not a real number

Question 6

Perform the indicated operation. Assume all variables represent positive numbers.  (9x−12) −12\left( 9 x ^ { - 12 } \right)  ^ { - \frac { 1 } { 2 } }(9x−12) −21​

Accepted Answer

A)    −3x6- 3 x ^ { 6 }−3x6 
B)    x63\frac { x ^ { 6 } } { 3 }3x6​ 
C)    9x69 x ^ { 6 }9x6 
D)    13x6\frac { 1 } { 3 x ^ { 6 } }3x61​

Question 7

Find the missing lengths in the triangle. Give the answer to two decimal places.  x= __________ y= __________

Accepted Answer

The answer of Find the missing lengths in the triangle....

Question 8

Simplify the expression. $i^{29}$

Accepted Answer

The answer of Simplify the expression. $i^{29}$...

Question 9

The lengths of two sides of the right triangle ABC are given. Find the length of the missing side. a=3 ft and b=4 ft

c= __________ ft

Accepted Answer

The answer of The lengths of two sides of the...

Question 10

Rationalize the denominator.  3+23−2\frac { \sqrt { 3 } + \sqrt { 2 } } { \sqrt { 3 } - \sqrt { 2 } }3​−2​3​+2​​

Accepted Answer

A)    −5−26- 5 - 2 \sqrt { 6 }−5−26c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
B)    5+265 + 2 \sqrt { 6 }5+26c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
C)    56+15 \sqrt { 6 } + 156c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​+1 
D)    −5+26- 5 + 2 \sqrt { 6 }−5+26c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
E)    5−265 - 2 \sqrt { 6 }5−26c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​

Question 11

Perform the operation. Write the answer in the form $a + b i$ . $( 6 + \sqrt { - 4 } ) + ( 8 + \sqrt { - 9 } )$

Accepted Answer

The answer of Perform the operation. Write the answer in...

Question 12

Multiply. $\sqrt { - 2 } \sqrt { - 14 }$

Accepted Answer

The answer of Multiply. \(\sqrt { - 2 } \sqrt...

Question 13

Perform the indicated operation. Simplify, if possible.  3x96x4−4486x543 x \sqrt [ 4 ] { 96 x } - 4 \sqrt [ 4 ] { 486 x ^ { 5 } }3x496x​−44486x5​

Accepted Answer

A)    6x6x46 x \sqrt [ 4 ] { 6 x }6x46xc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
B)    −6x6x4- 6 x \sqrt [ 4 ] { 6 x }−6x46xc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
C)    12x6x412 x \sqrt [ 4 ] { 6 x }12x46xc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
D)    −3x46x- 3 x ^ { 4 } \sqrt { 6 x }−3x46xc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​

Question 14

Perform the operation. Write the answer in the form $a + b i$ . $( 3 + 4 i ) + ( 5 - 9 i )$

Accepted Answer

The answer of Perform the operation. Write the answer in...

Question 15

Solve: $\sqrt { x } + 2 = \sqrt { 2 x + 7 }$

Accepted Answer

The answer of Solve: \(\sqrt { x } + 2...

Question 16

Square the quantity and simplify the result, if possible. $( 2 \sqrt { 2 r } - 1 ) ^ { 2 }$

Accepted Answer

The answer of Square the quantity and simplify the result,...

Question 17

Multiply. Write the answer in the form $a + b i$ . $( 5 - 3 i ) ( 3 + 5 i )$

Accepted Answer

The answer of Multiply. Write the answer in the form...

Question 18

Simplify:  163216 ^ { \frac { 3 } { 2 } }1623​

Accepted Answer

A)    164\frac { 1 } { 64 }641​ 
B)   -64
C)   not a real number
D)   64

Question 19

Simplify the expression. Assume that x is unrestricted and use absolute value symbols if necessary. $\sqrt { 9 x ^ { 2 } }$

Accepted Answer

The answer of Simplify the expression. Assume that x is...

Question 20

The __________ of $\sqrt { x } + 3$ is $\sqrt { x } - 3$ .

Accepted Answer

The answer of The __________ of \(\sqrt { x }...

Exam 7: Radical Expressions and Equations

Rationalize the denominator. 3+23−2\frac { \sqrt { 3 } + \sqrt { 2 } } { \sqrt { 3 } - \sqrt { 2 } }3​−2​3​+2​​

Correct AnswerverifiedShow Answer

Simplify the expression. i29i^{29}i29

Correct AnswerverifiedShow Answer

Simplify the expression. Assume that x is unrestricted and use absolute value symbols if necessary. 9x2\sqrt { 9 x ^ { 2 } }9x2​

Correct AnswerverifiedShow Answer

Solve: x+2=2x+7\sqrt { x } + 2 = \sqrt { 2 x + 7 }x​+2=2x+7​

Correct AnswerverifiedShow Answer

Square the quantity and simplify the result, if possible. (22r−1)2( 2 \sqrt { 2 r } - 1 ) ^ { 2 }(22r​−1)2

Correct AnswerverifiedShow Answer

Multiply: 64⋅68\sqrt [ 4 ] { 6 } \cdot \sqrt [ 8 ] { 6 }46​⋅86​

Correct AnswerverifiedShow Answer

Perform the operation. Write the answer in the form a+bia + b ia+bi . (6+−4)+(8+−9)( 6 + \sqrt { - 4 } ) + ( 8 + \sqrt { - 9 } )(6+−4​)+(8+−9​)

Correct AnswerverifiedShow Answer

Multiply. Write the answer in the form a+bia + b ia+bi . (5−3i)(3+5i)( 5 - 3 i ) ( 3 + 5 i )(5−3i)(3+5i)

Correct AnswerverifiedShow Answer

Square both sides of the equation. x+3+2=x−1\sqrt { x + 3 } + 2 = \sqrt { x - 1 }x+3​+2=x−1​

Correct AnswerverifiedShow Answer

The __________ of x+3\sqrt { x } + 3x​+3 is x−3\sqrt { x } - 3x​−3 .

Correct AnswerverifiedShow Answer

Perform the operation. Write the answer in the form a+bia + b ia+bi . (3+4i)+(5−9i)( 3 + 4 i ) + ( 5 - 9 i )(3+4i)+(5−9i)

Correct AnswerverifiedShow Answer

The lengths of two sides of the right triangle ABC are given. Find the length of the missing side. a=3 ft and b=4 ft c= __________ ft

Correct AnswerverifiedShow Answer

Perform the indicated operation. Assume all variables represent positive numbers. (9x−12) −12\left( 9 x ^ { - 12 } \right) ^ { - \frac { 1 } { 2 } }(9x−12) −21​

Correct AnswerverifiedShow Answer

Multiply. −2−14\sqrt { - 2 } \sqrt { - 14 }−2​−14​

Correct AnswerverifiedShow Answer

Find the missing lengths in the triangle. Give the answer to two decimal places. x= __________ y= __________

Correct AnswerverifiedShow Answer

Find f(−4) f ( - 4 ) f(−4) , given f(x) =x−233f ( x ) = \sqrt [ 3 ] { x - 23 }f(x) =3x−23​

Correct AnswerverifiedShow Answer

Multiply and simplify, if possible. 8mn3(5mn)8 \sqrt { m n ^ { 3 } } ( 5 \sqrt { m n } )8mn3​(5mn​)

Correct AnswerverifiedShow Answer

In the expression 27x63\sqrt [ 3 ] { 27 x ^ { 6 } }327x6​ , the index is 3 and 27x627 x ^ { 6 }27x6 is the __________.

Correct AnswerverifiedShow Answer

Perform the indicated operation. Simplify, if possible. 3x96x4−4486x543 x \sqrt [ 4 ] { 96 x } - 4 \sqrt [ 4 ] { 486 x ^ { 5 } }3x496x​−44486x5​

Correct AnswerverifiedShow Answer

Simplify: 163216 ^ { \frac { 3 } { 2 } }1623​

Correct AnswerverifiedShow Answer

Rationalize the denominator. $\frac { \sqrt { 3 } + \sqrt { 2 } } { \sqrt { 3 } - \sqrt { 2 } }$

Correct Answer
verified

Simplify the expression. $i^{29}$

Correct Answer
verified

Simplify the expression. Assume that x is unrestricted and use absolute value symbols if necessary. $\sqrt { 9 x ^ { 2 } }$

Correct Answer
verified

Solve: $\sqrt { x } + 2 = \sqrt { 2 x + 7 }$

Correct Answer
verified

Square the quantity and simplify the result, if possible. $( 2 \sqrt { 2 r } - 1 ) ^ { 2 }$

Correct Answer
verified

Multiply: $\sqrt [ 4 ] { 6 } \cdot \sqrt [ 8 ] { 6 }$

Correct Answer
verified

Perform the operation. Write the answer in the form $a + b i$ . $( 6 + \sqrt { - 4 } ) + ( 8 + \sqrt { - 9 } )$

Correct Answer
verified

Multiply. Write the answer in the form $a + b i$ . $( 5 - 3 i ) ( 3 + 5 i )$

Correct Answer
verified

Square both sides of the equation. $\sqrt { x + 3 } + 2 = \sqrt { x - 1 }$

Correct Answer
verified

The __________ of $\sqrt { x } + 3$ is $\sqrt { x } - 3$ .

Correct Answer
verified

Perform the operation. Write the answer in the form $a + b i$ . $( 3 + 4 i ) + ( 5 - 9 i )$

Correct Answer
verified

Correct Answer
verified

Perform the indicated operation. Assume all variables represent positive numbers. $\left( 9 x ^ { - 12 } \right) ^ { - \frac { 1 } { 2 } }$

Correct Answer
verified

Multiply. $\sqrt { - 2 } \sqrt { - 14 }$

Correct Answer
verified

Find the missing lengths in the triangle. Give the answer to two decimal places. x= y=

Correct Answer
verified

Find $f ( - 4 )$ , given $f ( x ) = \sqrt [ 3 ] { x - 23 }$

Correct Answer
verified

Multiply and simplify, if possible. $8 \sqrt { m n ^ { 3 } } ( 5 \sqrt { m n } )$

Correct Answer
verified

In the expression $\sqrt [ 3 ] { 27 x ^ { 6 } }$ , the index is 3 and $27 x ^ { 6 }$ is the __________.

Correct Answer
verified

Perform the indicated operation. Simplify, if possible. $3 x \sqrt [ 4 ] { 96 x } - 4 \sqrt [ 4 ] { 486 x ^ { 5 } }$

Correct Answer
verified

Simplify: $16 ^ { \frac { 3 } { 2 } }$

Correct Answer
verified