+44 Look for factors of 360 that are perfect squares or use a prime factorization method. I'm terrible at finding perfect squares as factors so I normally just divide by prime numbers until I get a prime number, it's extremely inefficient but it's simple and always works. 360/2 is 180, 180/2 is 90, 90/2 is 45, 45/5 = 9, 9/3 is 3. We found 2*2*2*5*3*3 = 360. So sqrt(360) is sqrt(2) * sqrt(2) * sqrt(2) * sqrt(5) * sqrt(3) * sqrt(3). Sqrt(2) * sqrt(2) is 2, so every pair of numbers comes outside the radical (square root symbol), so 2*3 is 6 and we have sqrt(2) * sqrt(5) left, so the simplified version is 6*sqrt(10). The fastest way was to realize that 360 = 36*10, and the sqrt(36) is 6. An easy way to check the solution is to square the outside term and multiply it by the term inside the radical (6*6*10 = 360, so our answer is right).
+44 Look for factors of 360 that are perfect squares or use a prime factorization method. I'm terrible at finding perfect squares as factors so I normally just divide by prime numbers until I get a prime number, it's extremely inefficient but it's simple and always works. 360/2 is 180, 180/2 is 90, 90/2 is 45, 45/5 = 9, 9/3 is 3. We found 2*2*2*5*3*3 = 360. So sqrt(360) is sqrt(2) * sqrt(2) * sqrt(2) * sqrt(5) * sqrt(3) * sqrt(3). Sqrt(2) * sqrt(2) is 2, so every pair of numbers comes outside the radical (square root symbol), so 2*3 is 6 and we have sqrt(2) * sqrt(5) left, so the simplified version is 6*sqrt(10). The fastest way was to realize that 360 = 36*10, and the sqrt(36) is 6. An easy way to check the solution is to square the outside term and multiply it by the term inside the radical (6*6*10 = 360, so our answer is right).
