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

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Answer 1 · 2016-06-15T12:40:38

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

#(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#