To simplify the square root of 48, follow these steps:
Step 1: Begin by finding the factors of 48. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
Step 2: Find the largest perfect square that divides evenly into 48. The largest perfect square that divides evenly into 48 is 16, which is equal to 4 squared.
Step 3: Rewrite the square root of 48 as the square root of 16 times the square root of 3. This is possible because the square root of a product is equal to the product of the square roots.
Step 4: Simplify the square root of 16, which is equal to 4.
Step 5: Simplify the square root of 3. Since 3 is not a perfect square, the square root of 3 cannot be simplified further.
Step 6: Putting it all together, the square root of 48 can be simplified as 4 times the square root of 3, which can be written as 4√3.
Therefore, the simplified form of the square root of 48 is 4√3.