# How do you simplify sqrt(4205)?

Feb 14, 2016

$= 29 \sqrt{5}$

#### Explanation:

Let's find out factors of the given number 4205

1. Since there is 5 in the units place, 5 must be a factor.
$4205 = 5 \times 841$
2. To find factors of 841, we observe 1 in the unit's place. So the factor could have either 1 or 9 in its units place.
Possible factors are 11, 19, 21, 29. By trial and error we find that 29 is a factor.
$4205 = 5 \times 29 \times 29$

Now the question becomes
$\sqrt{4205} = \sqrt{5 \times 29 \times 29}$

Taking 29 out of the square root sign

$= 29 \sqrt{5}$