How do you simplify #3sqrt50-3sqrt32#?

2 Answers
Feb 9, 2017

Answer:

#3sqrt(2)#

Explanation:

#3sqrt(50) - 3sqrt(32)#:

the surds in the question are not simplified. therefore they can be broken down further.

#3sqrt(50)#:

factors of #50#: #1,2,5,10,25,50.#

#sqrt(25) = 5#

#therefore 3sqrt(50)=3*sqrt(25)*sqrt(2)#
#=3*5*sqrt(2)#
#= 15sqrt(2)#

#3sqrt(32)#:

factors of #32#: #1,2,4,8,16,32#

#sqrt(16)=4#

#therefore 3sqrt(32)=3*sqrt(16)*sqrt(2)#
#=3*4*sqrt(2)#
#=12sqrt(2)#

the question is simplified to #15sqrt(2) - 12sqrt(2)#

law of surds:
#asqrt(b) + csqrt(b) = (a+c)sqrt(b)#

#15sqrt(2) + -12sqrt(2) = (15-12)sqrt(2)#
#=3sqrt(2)#

Feb 9, 2017

Answer:

#3sqrt2#

Explanation:

#3sqrt50-3sqrt32#

#:.=3*sqrt(2*5*5)-3*sqrt(2*2*2*2*2#

#:.=3*sqrt2*sqrt5*sqrt5-3*sqrt2*sqrt2*sqrt2*sqrt2*sqrt2#

note: #sqrt5*sqrt5=5# and# sqrt2*sqrt2=2#

#:.=3*sqrt2*5-3*2*2*sqrt2#

#:.=15*sqrt2-12*sqrt2#

#:.=3sqrt2(5-4)#

#:.=3sqrt2*1#

#:.=3sqrt2#