Question

What is the square root of cube root of 46656?

Answer 1

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.