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

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Answer 1 · 2016-06-01T13:23:57

#= color(Blue)(15 sqrt2 #

#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).

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 #