How do you simplify #(3sqrt5 + 2sqrt10) (4sqrt5 - 6sqrt10)#?

1 Answer
Jun 15, 2016

Answer:

#(3sqrt5+2sqrt10)(4sqrt5-6sqrt10)=130sqrt2-60#

Explanation:

#(3sqrt5+2sqrt10)(4sqrt5-6sqrt10)#

= #3sqrt5(4sqrt5+6sqrt10)+2sqrt10(4sqrt5-6sqrt10)#

= #12sqrt25+18sqrt50+8sqrt50-12sqrt100#

= #12sqrt(5xx5)+18sqrt(2xx5xx5)+8sqrt(2xx5xx5)-12sqrt(10xx10)#

= #12xx5+18xx5xxsqrt2+8xx5xxsqrt2-12xx10#

= #60+90xxsqrt2+40sqrt2-120#

= #130sqrt2-60#