How do you simplify $(4[sqrt5] )/( 7[sqrt2] - 7[sqrt5])$ ?

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Answer 1 · 2016-06-08T13:51:15

$(4sqrt5)/(7sqrt2-7sqrt5)=-(20+4sqrt10)/21$

$(4sqrt5)/(7sqrt2-7sqrt5)=(4sqrt5)/(7(sqrt2-sqrt5))$

Now multiplying numerator and denominator by $(sqrt2-sqrt5)$ , which is conjugate of denominator, we get

$(4sqrt5)/(7(sqrt2-sqrt5))xx(sqrt2+sqrt5)/(sqrt2+sqrt5)$

= $(4sqrt5(sqrt2+sqrt5))/(7(sqrt2-sqrt5)(sqrt2+sqrt5))$

= $(4sqrt10+4*5)/(7(2-5))$

= $(20+4sqrt10)/(7*(-3))$

= $-(20+4sqrt10)/21$

How do you simplify (4[sqrt5] )/( 7[sqrt2] - 7[sqrt5])(4[sqrt5] )/( 7[sqrt2] - 7[sqrt5])?