Question

How do you simplify `(4 sqrt12) * (3 sqrt20)`?

Answer 1

`= 48 sqrt ( 15)`

Explanation:

`(4 sqrt 12 ) * ( 3 sqrt 20)`

`= 4 * sqrt 12 * 3 * sqrt 20`

• Simplifying both `sqrt12` and `sqrt20` by prime factorisation.

Note: Prime factorisation is expressing a number as a product of its prime factors.

• `sqrt12 = sqrt (2 * 2 * 3) = sqrt (2^2 * 3 ) = color(green)(2 sqrt3`

• `sqrt20 = sqrt (2 * 2 * 5) = sqrt (2^2 * 5 ) = color(blue)(2 sqrt5`

`4 * sqrt 12 * 3 * sqrt 20 = 4 * color(green)(2 sqrt3) * 3 * color(blue)(2 sqrt5`

`4 * color(blue)(2) * sqrt3 * 3 * color(blue)(2 ) * sqrt5 = 4 * 3 * color(blue)( 2 * 2) * sqrt3 * sqrt5`

`= 48 sqrt3 * sqrt5`

`= 48 sqrt ( 3 * 5)`

`= 48 sqrt ( 15)`