How do you simplify #-sqrt338-sqrt200+sqrt162#?

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Answer 1 · 2018-04-13T21:46:06

#-14sqrt{2}#

You could try using the Fundamental Theorem of Arithmetic to express all those integers as the product of their primes.

#338 = 2^1 times 13^2#
#200 = 2^3 times 5^2#
#162 = 2^1 times 3^4#

What this tells us is that they all have a common factor of 2
#gcd(338,200,162)=2#

Since the expression contains the square root of each that means the entire expression has a factor of #sqrt{2}#, so we can rewrite it as

#sqrt{2} (-sqrt{13^2}-sqrt{2^2 5^2}+sqrt{3^4} )#
As we can see these all contain even powers and can thus be simplified!

#sqrt{2} (-13-10+9 )#

#sqrt{2} (-14)#

#-14sqrt{2}#