# How do you simplify 5sqrt(12)+sqrt(75)?

Apr 5, 2018

$15 \sqrt{3}$

#### Explanation:

Simplifying...

$\sqrt{75}$

$\to \sqrt{25} \times \sqrt{3}$

$\to 5 \sqrt{3}$

Simplifying again:

$5 \sqrt{12}$

$\to 5 \sqrt{4} \sqrt{3}$

$\to 5 \times 2 \sqrt{3}$

$\to 10 \sqrt{3}$

$5 \sqrt{3} + 10 \sqrt{3}$

Since the roots are the same, just add the numbers in front...

$\to 15 \sqrt{3}$

Apr 6, 2018

Given

$5 \sqrt{12} + \sqrt{75}$

Factorizing numbers under the root sign we get

$5 \sqrt{2 \times 2 \times 3} + \sqrt{3 \times 5 \times 5}$

Paring number which can be taken out of root sign

$5 \sqrt{\overline{2 \times 2} \times 3} + \sqrt{3 \times \overline{5 \times 5}}$
$\implies 5 \times 2 \sqrt{3} + \sqrt{3} \times 5$
$\implies 10 \sqrt{3} + 5 \sqrt{3}$
$\implies \sqrt{3} \left(10 + 5\right)$
$\implies 15 \sqrt{3}$