How do you simplify #30sqrt18-15sqrt50#?

1 Answer
Jun 1, 2016

Answer:

#= color(Blue)(15 sqrt2 #

Explanation:

#30 color(Blue)(sqrt18) -15 color(blue)(sqrt 50#

We simplify #color(blue)(sqrt18# and #color(blue)(sqrt50# by prime factorisation. (expressing a number as a product of prime factors).

  • #sqrt18 = sqrt ( 3 * 3 * 2 ) = sqrt ( 3^2 * 2) = color(blue)(3 sqrt2#

  • #sqrt50 = sqrt ( 2 * 5 * 5 ) = sqrt ( 5^2 * 2) = color(blue)(5 sqrt2#

The expression now becomes:

#30 color(Blue)(sqrt18) -15 color(blue)(sqrt 50) = 30 * color(blue)(3 sqrt2) -15 * color(blue)(5 sqrt2#

#= 90sqrt2 - 75sqrt2#

Since #sqrt2# is common to both terms we take it out as a common term,

#= sqrt2 ( 90 - 75) #

#= sqrt2 (15) #

#= color(Blue)(15 sqrt2 #