# How do you simplify 30sqrt18-15sqrt50?

Jun 1, 2016

= color(Blue)(15 sqrt2

#### Explanation:

30 color(Blue)(sqrt18) -15 color(blue)(sqrt 50

We simplify color(blue)(sqrt18 and color(blue)(sqrt50 by prime factorisation. (expressing a number as a product of prime factors).

• sqrt18 = sqrt ( 3 * 3 * 2 ) = sqrt ( 3^2 * 2) = color(blue)(3 sqrt2

• sqrt50 = sqrt ( 2 * 5 * 5 ) = sqrt ( 5^2 * 2) = color(blue)(5 sqrt2

The expression now becomes:

30 color(Blue)(sqrt18) -15 color(blue)(sqrt 50) = 30 * color(blue)(3 sqrt2) -15 * color(blue)(5 sqrt2

$= 90 \sqrt{2} - 75 \sqrt{2}$

Since $\sqrt{2}$ is common to both terms we take it out as a common term,

$= \sqrt{2} \left(90 - 75\right)$

$= \sqrt{2} \left(15\right)$

= color(Blue)(15 sqrt2