# How do you simplify 3sqrt(75)-5sqrt(100)?

Apr 11, 2018

$15 \sqrt{3} - 50$

#### Explanation:

Simply roots
$\sqrt{75}$=$\sqrt{3} \cdot \sqrt{25}$
=$5 \sqrt{3}$
$\sqrt{100} = 10$
Substitute back in
$3 \cdot 5 \sqrt{3} - 5 \cdot 10 = 15 \sqrt{3} - 50$

Apr 11, 2018

$15 \cdot \sqrt{3} - 50$

#### Explanation:

You use the rule that:

${\left(a b\right)}^{x} = {a}^{x} {b}^{x}$

In this case:

$3 \sqrt{75} - 5 \sqrt{100} = 3 \sqrt{25 \cdot 3} - 5 \cdot 10$

Using the above rule on the left hand part of the expression:

$3 \sqrt{25} \sqrt{3} - 5 \cdot 10 = 3 \cdot 5 \cdot \sqrt{3} - 50$

$= 15 \cdot \sqrt{3} - 50$