How do you simplify sqrt200-sqrt32?

2 Answers
May 7, 2016

6sqrt(2)

Explanation:

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

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

May 7, 2016

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