How do you simplify #3/sqrt(7)#?
1 Answer
Aug 9, 2016
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#