Question

How do you find the square root of 5625?

Answer 1

Split into prime factors, identify factors which occur in pairs, hence find: `5625 = 75^2`, so:

`sqrt(5625) = 75`

Explanation:

Start by finding prime factors of `5625`:

`2`: No: `5625` is odd.
`3`: Yes:
`color(white)(XX)5625 = 3 * 1875 = 3 * 3 * 625`
`5`: Yes:
`color(white)(XX)3 * 3 * 625 = 3 * 3 * 5 * 125 = 3 * 3 * 5 * 5 * 25`
`color(white)(XX)= 3 * 3 * 5 * 5 * 5 * 5 = (3*5*5)^2 = 75^2`

Answer 2

`sqrt5625=75`

Explanation:

As the number ends with `25 =5^2`, 5625, therefore, is a multiplum of 25.

I also recognise that `25^2=625`, which is the last part of 5625. I would, therefore, check if 5625 is a multiplum of 625:
`5625/625=9=3^2`

Therefore `5625=3^2*25^2=75^2`

Therefore `sqrt5625=75`