To simplify the square root of 8, we start by breaking it down into its prime factors. The number 8 can be expressed as 4 times 2, which is the same as 22 × 2.
Now, we can rewrite the square root of 8 as:
√8 = √(4 × 2) = √4 × √2
Since the square root of 4 is 2, we substitute that in:
√8 = 2 × √2
Thus, the simplified form of the square root of 8 is:
2√2
This means that √8 is equal to approximately 2.83 when you calculate it numerically. However, for exact values in simplification, it is more appropriate to leave it as 2√2.