Math, asked by freddymatthew, 4 months ago

Simplify the following in surds

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Answered by bson

1

Step-by-step explanation:

3×sqrt2 - 2xsqrt3/(3sqrt2 + 2sqrt3)

=(3sqrt2 - 2sqrt3)²/(3sqrt2 + 2sqrt3)×(3sqrt2+ 2sqrt3)

=(3sqrt2 - 2sqrt3)²/((3×sqrt2)²-(2sqrt3)²)

= 9×2 + 4x3 - 3xsqrt2x2xsqrt3 /(9×2 - 4x3)

=18+12-6sqrt6/(18-12) = 30-6sqrt6/6=6(5-sqrt6)/6

=5-sqrt6

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