How do you simplify -sqrt338-sqrt200+sqrt162?

1 Answer
Apr 13, 2018

-14sqrt{2}

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 13^2
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}