Question

What is the square root of 156.25?

Answer 1

`sqrt(156.25) = 25/2`

Explanation:

`15625 = 5^6`

So `156.25 = (5^6)/100 = (5^6)/(2^2*5^2) = 5^4/2^2`

If `a, b >= 0`, then `sqrt(a/b) = sqrt(a)/sqrt(b)`

If `a, b, c > 0` then `a^(bc) = (a^b)^c`

So `sqrt(156.25) = sqrt(5^4/2^2) = sqrt(5^4)/sqrt(2^2) = sqrt((5^2)^2)/sqrt(2^2) = 5^2/2 = 25/2`