How do you simplify #(5sqrt3)/(6sqrt10)#?

1 Answer
Mar 23, 2018

Answer:

#sqrt30/12#

Explanation:

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

#•color(white)(x)sqrtaxxsqrtbhArrsqrt(ab)#

#•color(white)(x)sqrtaxxsqrta=a#

#"to simplify we require to remove the radical from the "#
#"denominator"#

#"this is achieved by multiplying numerator/denominator"#
#"by "sqrt10#

#rArr(5sqrt3)/(6sqrt10)xxsqrt10/sqrt10#

#=(5xxsqrt(3xx10))/(6xxsqrt(10xx10))#

#=(5xxsqrt30)/(6xxsqrt100)=(cancel(5)^1xxsqrt30)/(cancel(60)^(12))=sqrt30/12#