# How do you find the square root of 5929?

Sep 8, 2015

Factor into primes to find:

$5929 = 7 \cdot 7 \cdot 11 \cdot 11 = {\left(7 \cdot 11\right)}^{2} = {77}^{2}$

So $\sqrt{5929} = 77$

#### Explanation:

Let's look for prime factors:

$2$ - No - it's not even.
$3$ - No - the digits don't add up to a multiple of $3$.
$5$ - No - it doesn't end with $5$ or $0$.
$7$ - Yes:

$5929 = 7 \cdot 847 = 7 \cdot 7 \cdot 121 = 7 \cdot 7 \cdot 11 \cdot 11 = {\left(7 \cdot 11\right)}^{2} = {77}^{2}$