How do you simplify #sqrt200-sqrt32#?

2 Answers
May 7, 2016

Answer:

#6sqrt(2)#

Explanation:

#sqrt(2xx10^2)-sqrt(2xx4^2)#

#10sqrt(2)-4sqrt(2)#
'~~~~~~~~~~~~~~~~~~~~~~
compare to #10x-4x=6x#
'~~~~~~~~~~~~~~~~~~~~~~~~~~
#=>6sqrt(2)#

May 7, 2016

Answer:

#6sqrt2#

Explanation:

Breaking the values down into the prime factors is always possible, but sometimes a bit tedious and often unnecessary if square numbers are recognised as being factors. 200 = 100 x 2 is an obvious example.

#sqrt200 - sqrt32#
= #sqrt(100xx2) - sqrt(16xx2#
= #10sqrt2 - 4sqrt2#
= #sqrt2(10-4)#
= #6sqrt2#