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Question 1 of 5
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Find factors that are perfect squares for √162a√162a
| 8√162a8√162a |
== |
8√81×2×a8√81×2×a |
Factor by finding the greatest perfect square of 162162 |
|
== |
8×√81×√2×√a8×√81×√2×√a |
Apply the Multiplication Property |
|
== |
8×9×√2×√a8×9×√2×√a |
8181 is a perfect square |
|
== |
72×√2×√a72×√2×√a |
|
== |
72√2a72√2a |
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Question 2 of 5
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First, separate the variable from the constant.
| √24x2√24x2 |
== |
√24√24××√x2√x2 |
Apply the Multiplication Property |
Next, simplify the variable by rewriting the square root in √x2 as a fractional exponent
| √x2 |
= |
(x2)12 |
|
= |
x |
Use the Power Rule to simplify (xa)b=xab |
Finally, find factors that are perfect squares for √24×x
| √24×x |
= |
√4×6×x |
|
= |
√4×√6×x |
Apply the Multiplication Property |
|
= |
2×√6×x |
4 is a perfect square |
|
= |
2x√6 |
Rearrange the expression |
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Question 3 of 5
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First, separate the variable from the constant.
| √16x3 |
= |
√16×√x3 |
Apply the Multiplication Property |
Next, simplify the variable by rewriting the square root in √x3 as a fractional exponent
| √x3 |
= |
√x2×x |
| √x3 |
= |
√x2×√x |
Apply the Multiplication Property |
|
= |
x×√x |
Use the Power Rule to simplify (xa)b=xab |
|
= |
x√x |
Finally, find factors that are perfect squares for √16×x√x
| √16×x√x |
= |
4×x |
|
= |
4x√x |
Rearrange the expression |
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Question 4 of 5
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First, separate the variable from the constant.
| √9(y+7)4 |
= |
√9×√(y+7)4 |
Apply the Multiplication Property |
Next, get the factor of √(y+7)4 and simplify
| √(y+7)4 |
= |
√(y+7)2×(y+7)2 |
|
= |
(y+7)2 |
(y+7)4 is a perfect square |
Finally, find factors that are perfect squares for √9×(y+7)2
| √9×(y+7)2 |
= |
3×(y+7)2 |
|
= |
3(y+7)2 |
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Question 5 of 5
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Find factors that are perfect squares for √x7
| √x7 |
= |
√x6×√x |
Find the highest even factor of x7 |
|
= |
x3×√x |
√x6 is a perfect square |
|
= |
x3√x |
