How do you simplify (sqrt 5 + 9 sqrt2)(4 sqrt5 - sqrt 2)(√5+9√2)(4√5−√2)?

1 Answer
ali ergin
May 29, 2016

(sqrt5+9sqrt2)(4sqrt5-sqrt2)=2+35sqrt10(√5+9√2)(4√5−√2)=2+35√10

Explanation:

(sqrt5+9sqrt2)(4sqrt5-sqrt2)(√5+9√2)(4√5−√2)

=4sqrt5*sqrt5-sqrt5*sqrt2+9sqrt2*4sqrt5-9sqrt2*sqrt2=4√5⋅√5−√5⋅√2+9√2⋅4√5−9√2⋅√2

=4(sqrt5)^2-sqrt10+36sqrt10-9(sqrt2)^2=4(√5)2−√10+36√10−9(√2)2

=4*5+35sqrt10-9*2=4⋅5+35√10−9⋅2

=20+35sqrt10-18=20+35√10−18

=2+35sqrt10=2+35√10

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