How do you simplify 3/sqrt(7)?

1 Answer
Jim G.
Aug 9, 2016

(3sqrt7)/7

Explanation:

Simplifying this fraction means expressing it without the radical on the denominator. This is called color(blue)"rationalising the denominator"

To do this we make use of the following fact.

color(red)(|bar(ul(color(white)(a/a)color(black)(sqrtaxxsqrta=(sqrta)^2=a)color(white)(a/a)|)))

rArrsqrt7xxsqrt7=7

Since this is a fraction, if we multiply the denominator by some value then we must multiply the numerator by the same value.

multiply both numerator and denominator by sqrt7

rArr3/sqrt7xxsqrt7/sqrt7=(3xxsqrt7)/(sqrt7xxsqrt7)=(3sqrt7)/7

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