How do you simplify (3+√5)×(5−√5)?

1 Answer
Jim G.
Jun 4, 2016

10+2√5

Explanation:

By expanding the brackets using FOIL or similar method.

⇒(3+√5)(5−√5)=15−3√5+5√5−(√5)2
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now in general √a×√a=a

⇒(√5)2=√5×√5=5

radicals may be collected together in a similar manner to 'collecting like terms' algebraically.

That is 4√3+5√3=(4+5)√3=9√3

⇒−3√5+5√5=(−3+5)√5=2√5
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⇒(3+√5)(5−√5)=15−3√5+5√5−(√5)2

=15+2√5−5=10+2√5

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