How do you simplify -sqrt338-sqrt200+sqrt162338200+162?

1 Answer
Apr 13, 2018

-14sqrt{2}142

Explanation:

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

338 = 2^1 times 13^2338=21×132
200 = 2^3 times 5^2200=23×52
162 = 2^1 times 3^4162=21×34

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

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

sqrt{2} (-sqrt{13^2}-sqrt{2^2 5^2}+sqrt{3^4} )2(1322252+34)
As we can see these all contain even powers and can thus be simplified!

sqrt{2} (-13-10+9 )2(1310+9)

sqrt{2} (-14)2(14)

-14sqrt{2}142