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How do you simplify #3/sqrt(7)#?

Answer 1

#(3sqrt7)/7#

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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Answer 2

Jace Anderson

To simplify 3/sqrt(7), you can multiply both the numerator and denominator by sqrt(7). This results in (3 * sqrt(7))/(sqrt(7) * sqrt(7)), which simplifies to (3 * sqrt(7))/7.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.