# How do you find the square root of 5625?

Sep 8, 2015

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:
$\textcolor{w h i t e}{X X} 5625 = 3 \cdot 1875 = 3 \cdot 3 \cdot 625$
$5$: Yes:
$\textcolor{w h i t e}{X X} 3 \cdot 3 \cdot 625 = 3 \cdot 3 \cdot 5 \cdot 125 = 3 \cdot 3 \cdot 5 \cdot 5 \cdot 25$
$\textcolor{w h i t e}{X X} = 3 \cdot 3 \cdot 5 \cdot 5 \cdot 5 \cdot 5 = {\left(3 \cdot 5 \cdot 5\right)}^{2} = {75}^{2}$

Jul 3, 2018

$\sqrt{5625} = 75$

#### 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:
$\frac{5625}{625} = 9 = {3}^{2}$

Therefore $5625 = {3}^{2} \cdot {25}^{2} = {75}^{2}$

Therefore $\sqrt{5625} = 75$