SOLUTION: {{{17sqrt(20)}}} {{{-7sqrt(242)}}} {{{3sqrt(75)}}}

Algebra ->  Radicals -> SOLUTION: {{{17sqrt(20)}}} {{{-7sqrt(242)}}} {{{3sqrt(75)}}}      Log On


   



Question 164461: 17sqrt%2820%29
-7sqrt%28242%29
3sqrt%2875%29

Answer by Edwin McCravy(20086) About Me  (Show Source):
You can put this solution on YOUR website!

17+sqrt%2820%29

Break 20 down into a product of prime numbers:

20=2%2A2%2A5

17sqrt%282%2A2%2A5%29

Group the pair of like factors:

 17sqrt%28%282%2A2%29%2A5%29

The pair of like factors 2%2A2 can be written as 
a square 2%5E2

 17sqrt%28%282%5E2%29%2A5%29

Take individual square roots:

17sqrt%282%5E2%29sqrt%285%29

The square root of the square of 2 gives only 2:

17%2A2sqrt%285%29

34sqrt%285%29

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-7+sqrt%28242%29

Break 242 down into a product of prime numbers:

20=2%2A11%2A11

-7sqrt%282%2A11%2A11%29

Group the pair of like factors:

 -7sqrt%282%2A%2811%2A11%29%29

The pair of like factors 11%2A11 can be written as 
a square 11%5E2

 -7sqrt%282%2A11%5E2%29

Take individual square roots:

-7sqrt%282%29%2Asqrt%2811%5E2%29

The square root of the square of 11 gives only 11:

-7sqrt%282%29%2A11

-77sqrt%282%29

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3 SQRT 75

3+sqrt%2875%29

Break 75 down into a product of prime numbers:

75=3%2A5%2A5

3sqrt%283%2A5%2A5%29

Group the pair of like factors:

 3sqrt%283%2A%285%2A5%29%29

The pair of like factors 5%2A5 can be written as 
a square 5%5E2

 3sqrt%283%2A%285%5E2%29%29

Take individual square roots:

3sqrt%283%29sqrt%285%5E2%29

The square root of the square of 5 gives only 5:

3sqrt%283%29%2A5

15sqrt%283%29

Edwin