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Question 1 of 4
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First, separate the variable from the constant.
| √8a7 |
= |
√8×√a7 |
Apply the Multiplication Property |
Find factors that are perfect squares for √a7
| √a7 |
= |
√a6×a |
|
= |
a3√a |
a6 is a perfect square |
Simplify the values further
| √8×a3√a |
= |
√4×2×a3√a |
|
= |
2√2×a3√a |
4 is a perfect square |
|
= |
2a3√2a |
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Question 2 of 4
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First, separate the variable from the constant.
| 3√54y4 |
= |
3√54×3√y4 |
Apply the Multiplication Property |
Find factors that are perfect cubes for 3√y4
| 3√y4 |
= |
3√y3×y |
|
= |
y3√y |
y3 is a perfect cube |
Simplify the values further
| 3√54×y3√y |
= |
3√27×2×y3√y |
|
= |
3√27×3√2×y3√y |
Apply the Multiplication Property |
|
= |
3×3√2×y3√y |
27 is a perfect cube |
|
= |
3y×3√2×y |
Combine the terms |
|
= |
3y3√2y |
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Question 3 of 4
Incorrect
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First, separate the variable from the constant.
| √405a6b3 |
= |
√405×√a6b3 |
Apply the Multiplication Property |
Find factors that are perfect squares for √a6b3
| √a6b3 |
= |
a3√b3 |
a6 is a perfect square |
|
= |
a3√b2×b |
|
= |
a3×√b2×√b |
Apply Multiplication Property |
|
= |
a3b√b |
b2 is a perfect square |
Simplify the values further
| √405×a3b√b |
= |
√81×5×a3b√b |
|
= |
9×√5×a3b×√b |
81 is a perfect square |
|
= |
9a3b×√5b |
Combine like terms |
|
= |
9a3b√5b |
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Question 4 of 4
Simplify
3√−8x6y12
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First, separate the variable from the constant.
| 3√−8x6y12 |
= |
3√−8×3√x6y12 |
Apply the Multiplication Property |
Find factors that are perfect cubes for 3√x6y12
|
= |
3√(x2)3(y4)3 |
Cube root cancels the power |
|
= |
x2y4 |
Simplify the values further
| 3√−8×x2y4 |
= |
−2×x2y4 |
−8 is a perfect cube |
|
= |
−2x2y4 |
