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

1 Answer
Jun 8, 2016

Answer:

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

Explanation:

#(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#