# What is the square root of 169?

Sep 13, 2015

13

#### Explanation:

Aug 31, 2016

$169 = 13$

This is the principal root.
The root can be $\pm 13$

#### Explanation:

We are looking for a number which, multiplied by itself makes 169.

${x}^{2} = 169$

It is a huge advantage in your Maths to know all the squares up to ${20}^{2}$ by heart.

${12}^{2} = 144$
${13}^{2} = 169$

Bu estimating....

${10}^{2} = 100 \mathmr{and} {20}^{2} = 400$

So, $\sqrt{169}$ lies between 10 and 20.
If you find it by estimating, the number 9 at the end means that the square root must end in a 3 or a 7.

The only options are ${13}^{2} \mathmr{and} {17}^{2}$
Multiplying gives ${13}^{2} = 169 \mathmr{and} {17}^{2} = 289$