How do you find the square root of 81/16?

1 Answer
Jun 7, 2016

Answer:

#= color(blue)(9/4#

Explanation:

#sqrt (81/16)#

We simplify #81# and #16# by prime factorisation (expressing a number as a product of its prime factors).

  • #sqrt (81) = sqrt (3 * 3 * 3 * 3 ) = sqrt ( 9 * 9 ) = sqrt (9^2) = color(blue)(9#

  • #sqrt (16) = sqrt (2 * 2 * 2 * 2 ) = sqrt ( 4 * 4 ) = sqrt (4^2) = color(blue)(4#

So, #sqrt (81/16) = color(blue)(9/4#