# What is the square root of 10404?

Sep 8, 2015

102

#### Explanation:

To do it yourself factor it to primes and pull repeated numbers out of the square root:

$\sqrt{10404} = \sqrt{2 \cdot 2 \cdot 3 \cdot 3 \cdot 17 \cdot 17} = 2 \cdot 3 \cdot 17 = 102$

Sep 8, 2015

$\sqrt{10404} = 102$
$10404 = 10000 + 400 + 4 = {100}^{2} + \left(2 \cdot 100 \cdot 2\right) + {2}^{2}$
$= {\left(100 + 2\right)}^{2} = {102}^{2}$
Notice that ${12}^{2} = 144$, ${102}^{2} = 10404$, ${1002}^{2} = 1004004$, etc.