# What is the squared root of 14400?

Dec 2, 2015

=color(blue)(120

#### Explanation:

$\sqrt{14400}$

We prime factorise the number first (express the number as a product of primes):

$\sqrt{14400} = \sqrt{2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5 \cdot 5}$

$= \sqrt{{2}^{6} \cdot {3}^{2} \cdot {5}^{2}}$

=(2^6 * 3^2 * 5^2)^(color(blue)(1/2

$= \left({2}^{6 \cdot \frac{1}{2}}\right) \cdot \left({3}^{2 \cdot \frac{1}{2}}\right) \cdot \left({5}^{2 \cdot \frac{1}{2}}\right)$

=color(blue)(2^3*3*5

=color(blue)(120