Question

simplify √250-√117+3√40-5√52
will give medal

Answer 1

2) To simplify √250 - √117 + 3√40 - 5√52, first find the prime factorization for the value under each radical sign:
250 = 2•5•5•5
117 = 3•3•13
40 = 2•2•2•5
52 = 2•2•13
Next, when taking an n-th root, bring out factors which occur n times:
√250 = √(2•5•5•5) = 5√(2•5) = 5√10
√117 = √(3•3•13) = 3√13
√40 = √(2•2•2•5) = 2√(2•5) = 2√10
√52 = √(2•2•13) = 2√13
Rewrite the original expression using the equivalent terms:
√250 - √117 + 3√40 - 5√52 is now
5√10 - 3√13 + 3•2√10 - 5•2√13
Collect like terms:
(5 + 3•2)√10 - (3 + 5•2)√13
Simplify:
11√10 - 13√13

And how about fan reward
:D