How do you simplify the square root of 308?

Answer 1

Break 308 down into an equation that multiplies prime numbers together that equals 308. In the example, it would be the square root of (2x2x7x11). Because there are two 2's in the equation, pull them out from under the square root symbol. Then you have 2sqrt(7x11). Because there are no more doubles under the square root symbol, the simplified form of sqrt(308) is 2sqrt(77).

This is how I simplify radicals. Usually I just (if it's an even number) divide by two until I can't anymore, then divide by 3, and simplify from there. Whenever you get two of the same numbers, pull them outside the square root. Any numbers that don't have doubles stay under the square root, and are multiplied together.