Irrational confusion

Algebra Level 1

Evaluate:

( 2 2 + 5 3 − 7 5 ) + ( 3 3 − 2 + 5 ) (2\sqrt{2} + 5\sqrt{3} - 7\sqrt{5})+(3\sqrt{3}-\sqrt{2}+\sqrt{5})

2 + 8 3 − 6 5 \sqrt{2}+8\sqrt{3}-6\sqrt{5} 2 + 8 4 − 6 5 \sqrt{2}+8\sqrt{4}-6\sqrt{5} 2 − 6 3 − 6 5 \sqrt{2}-6\sqrt{3}-6\sqrt{5} 8 + 8 3 − 6 2 \sqrt{8}+8\sqrt{3}-6\sqrt{2}

Kishan Saxena by Kishan Saxena , 19, India

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2 solutions

Jack Rawlin
Oct 12, 2015

( 2 2 + 5 3 − 7 5 ) + ( 3 3 − 2 + 5 ) (2\sqrt{2} + 5\sqrt{3} - 7\sqrt{5}) + (3\sqrt{3} - \sqrt{2} + \sqrt{5})

  1. Putting like terms together gives us

( 2 2 − 2 ) + ( 5 3 + 3 3 ) + ( − 7 5 + 5 ) (2\sqrt{2} - \sqrt{2}) + (5\sqrt{3} + 3\sqrt{3}) + (-7\sqrt{5} + \sqrt{5})

  1. Then simplifying

2 + 8 3 − 6 5 \boxed{\sqrt{2} + 8\sqrt{3} - 6\sqrt{5}}

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Kishan Saxena
Mar 27, 2015

2√2+5√3-7√5+3√3-√2+√5

2√2-√2+5√3+3√3+√5-7√5

By taking common terms :- (2-1)√2+(5+3)√3+(1-7)√5

√2+8√3-6√5

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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