Question

How do you simplify `30sqrt18-15sqrt50`?

Answer 1

`= 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`

`= 90sqrt2 - 75sqrt2`

Since `sqrt2` is common to both terms we take it out as a common term,

`= sqrt2 ( 90 - 75)`

`= sqrt2 (15)`

`= color(Blue)(15 sqrt2`