Question

What is `\sqrt{\frac{36}{169}}`?

Answer 1

`+-6/13`

Explanation:

The `color(blue)"square root"` of a number is the value that, when multiplied by itself gives the number in the square root.

That is `6xx6" and " (-6)xx(-6)=36`

`rArrsqrt36=6" or " -6" written " +-6`

and `sqrt169=+-13`

`rArrsqrt(36/169)=+-6/13`

Answer 2

`sqrt(36/169) = sqrt36/sqrt169 = 6/13`

Explanation:

You might recognise that 36 and 169 are both 'square' numbers, formed by multiplying a number by itself.

`6xx6 =6^2 = 36` We can also say `sqrt36 =6`

`13xx13 =13^2 = 169` This means that `sqrt169 = 13`

We have: `sqrt(36/169)`

Although square roots often act like brackets, in this case you do not have to work out the answer to `36/169` first

We can split `sqrt(36/169)` into two separate square roots.

`sqrt(36/169) = sqrt36/sqrt169 = 6/13`

Later you will learn that there can be negative answers as well.