# How do you simplify sqrt(72/3)?

May 22, 2018

$2 \sqrt{6}$

#### Explanation:

$\text{using the "color(blue)"law of radicals}$

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$\Rightarrow \sqrt{\frac{72}{3}} = \sqrt{24} = \sqrt{4 \times 6} = \sqrt{4} \times \sqrt{6} = 2 \sqrt{6}$

May 22, 2018

$2 \sqrt{6}$

#### Explanation:

The goal in simplifying a square root is to divide the terms into their common factors.

This can be done in the following way.

Firstly you divide the radicand to get the simplest term: 24 ($\frac{72}{3}$)

Now, you find the common factors of 24.

1. 24 is made up of $6 \cdot 4$ or $3 \cdot 8$

6 factors into $2 \cdot 3$ and 4 factors into ${2}^{2}$ == ${2}^{3} \cdot 3$
3 is a factor of itself and 8 factors into ${2}^{3}$ == ${2}^{3} \cdot 3$

As you can see, either way you will get to the same result.

$\sqrt{{2}^{3} \cdot 3} = {\left({2}^{3} \cdot 3\right)}^{\frac{1}{2}} =$ exponent rule = ${2}^{3 + \left(\frac{1}{2}\right)} \cdot {3}^{\frac{1}{2}}$

Rewriting this equation we get:
${2}^{\frac{5}{2}} \cdot {3}^{\frac{1}{2}}$ == ${2}^{2} \cdot \left({2}^{\frac{1}{2}} \cdot {3}^{\frac{1}{2}}\right)$

Applying the square root (or factoring out the exponents)we get:

sqrt(2^2 * (2 *3) == $2 \sqrt{2 \cdot 3}$ == $2 \sqrt{6}$

May 22, 2018

$2 \sqrt{6}$

#### Explanation:

dividing under a radical is allowed:

$\sqrt{\frac{72}{3}} = \sqrt{24} = \sqrt{4 \cdot 6} = \sqrt{{2}^{2} \cdot 6} = 2 \sqrt{6}$

May 22, 2018

$2 \sqrt{6}$

#### Explanation:

$\sqrt{\frac{72}{3}} = \sqrt{24}$

$\Rightarrow \sqrt{24} = \sqrt{4} \times \sqrt{6}$

$\Rightarrow 2 \sqrt{6}$