Rationalize the denominator 5 over radical sighn 3 - 1?

Question

Thanks guys

Answer 1

5 /√3 - 1=

5 / √2 =

5√2 / √2 √2 =

5√2 / √4 =

5 √2 / 2

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Answer 2

Since (a + b)(a - b) = a^2 - b^2, you can "move" a sum or difference of square roots (or a square root and a rational) from the denominator to the numerator (or vice versa) by multiplying both top and bottom by the a +/- b term with sign opposite to the one you are trying to rationalize.

So for 5 over (sqrt(3) - 1), you move the square root in the difference from bottom to top by mutiplying both bottom and top by the corresponding sum:

= (5 times (sqrt(3) + 1)) over ((sqrt(3) - 1) times (sqrt(3) + 1))

The denominator simplifies to
( sqrt(3) )^2 - 1^2 = 3 - 1 = 2.

Dan

Answer 3

(5sqrt(2))/2