What is the square root of 24?

Mar 24, 2018

$2 \sqrt{6}$

Explanation:

Given: $\sqrt{24}$

We split it into the following:

$= \sqrt{4 \cdot 6}$

Now, we use the radical rule which states that, $\sqrt{a b} = \sqrt{a} \cdot \sqrt{b} , a , b > 0$.

So, we get,

$= \sqrt{4} \cdot \sqrt{6}$

$= 2 \sqrt{6}$

Mar 24, 2018

$\sqrt{24} = 2 \sqrt{6}$

Explanation:

We should try to reduce $\sqrt{24}$ to the root of a number with a perfect square multiplied by some other whole number.

Let's consider the factors of $24 :$

$1 , 4 , 6 , 8 , 12 , 24$

Out of these, $4$ is the largest (and coincidentally, only) perfect square present.

$4 \cdot 6 = 24 ,$ so we can rewrite as

$\sqrt{24} = \sqrt{4 \cdot 6} = \sqrt{4} \cdot \sqrt{6}$ as $\sqrt{a b} = \sqrt{a} \cdot \sqrt{b}$

Simplify:

$\sqrt{4} \cdot \sqrt{6} = 2 \sqrt{6}$