How to simplify 5x√(3y²/2) - 3y√(8x²/3) + 2√(3x²y²/2)?
Simplify 5x√(3y²/2) - 3y√(8x²/3) + 2√(3x²y²/2)
The answer is 3/2*xy*√6
But I didn't get that answer, here's what I did:
5x√(3y²/2) - 3y√(8x²/3) + 2√(3x²y²/2)
=xy√(25)(3/2) - xy√(9)(8/3) + xy√(4)(3/2)
=xy√(75/2 - 24 + 6)
=xy√(39/2)
Which part did I make a mistake?
Help :(
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Verified answer
Your mistake was in taking
√(75/2) - √24 + √6
to be equal to
√(75/2 - 24 + 6)
when in fact √(a+b) is not equal to √a + √b unless one of a, b is 0.
Instead, simplify √24 to 2√6, and
√(75/2)
= √(150/4)
= √(25*6) / 2
= (5/2)√6
and then since 5/2 - 2 + 1 = 3/2
we get (3/2)√6 agreeing with the given answer.