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Question
What is the square root of cube root of 46656?
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Solution
| 2 | 46656 |
| 2 | 23328 |
| 2 | 11664 |
| 2 | 5832 |
| 2 | 2916 |
| 2 | 1458 |
| 3 | 729 |
| 3 | 243 |
| 3 | 81 |
| 3 | 27 |
| 3 | 9 |
| 3 | 3 |
| 1 |
We have to find out `sqrt((root(3)(46656))`
First we will find `root(3)(46656)`
`root(3)(46656) = (bar(2 xx 2 xx 2) xx bar(2 xx 2 xx 2) xx bar(3 xx 3 xx 3) xx bar(3 xx 3 xx 3))^(1/3)`
`root(3)(46656)` = 2 × 2 × 3 × 3
`root(3)(46656)` = 22 × 32 = 36
Now `sqrt((root(3)(46656))) = sqrt(36)`
= `sqrt(2^2 xx 3^2)`
= 2 × 3
= 6
∴ The required number is 6.
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