How do you simplify #sqrt 2 / sqrt 10#?

1 Answer
Jim G.
Aug 14, 2017

#sqrt5/5#

Explanation:

#"to simplify a fraction with radicals we make the denominator"#
#"rational, that is remove the radical"#

#"using the "color(blue)"laws of radicals"#

#•color(white)(x)sqrtaxxsqrta=a#

#•color(white)(x)sqrtaxxsqrtbhArrsqrtab#

#"to remove the radical from the denominator multiply the"#
#"numerator and denominator by "sqrt10#

#sqrt2/sqrt10xxsqrt10/sqrt10#

#=sqrt(2xx10)/10#

#=sqrt20/10=sqrt(4xx5)/10=(sqrt4xxsqrt5)/10=(2sqrt5)/10=sqrt5/5#

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