How do you simplify (4 sqrt12) * (3 sqrt20)(4√12)⋅(3√20)?

1 Answer
Don't Memorise
May 27, 2016

= 48 sqrt ( 15) =48√15

Explanation:

(4 sqrt 12 ) * ( 3 sqrt 20)(4√12)⋅(3√20)

= 4 * sqrt 12 * 3 * sqrt 20 =4⋅√12⋅3⋅√20

  • Simplifying both sqrt12√12 and sqrt20√20 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√12=√2⋅2⋅3=√22⋅3=2√3

  • sqrt20 = sqrt (2 * 2 * 5) = sqrt (2^2 * 5 ) = color(blue)(2 sqrt5√20=√2⋅2⋅5=√22⋅5=2√5

4 * sqrt 12 * 3 * sqrt 20 = 4 * color(green)(2 sqrt3) * 3 * color(blue)(2 sqrt5 4⋅√12⋅3⋅√20=4⋅2√3⋅3⋅2√5

4 * color(blue)(2) * sqrt3 * 3 * color(blue)(2 ) * sqrt5 = 4 * 3 * color(blue)( 2 * 2) * sqrt3 * sqrt5 4⋅2⋅√3⋅3⋅2⋅√5=4⋅3⋅2⋅2⋅√3⋅√5

= 48 sqrt3 * sqrt5 =48√3⋅√5

= 48 sqrt ( 3 * 5) =48√3⋅5

= 48 sqrt ( 15) =48√15

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