Simplify √8.

Simplify √8.

• A. √8
• B. 2√2
• C. 4√2
• D. √2

Answer: (B)

The main idea is to pull out any square factors from under the square root. For √8, find a perfect square that divides 8. Since 8 = 4 × 2 and 4 is a perfect square, you can rewrite the radical as √(4×2) = √4 × √2 = 2 × √2 = 2√2. This is the simplest form because there are no more perfect-square factors inside the radical. Leaving it as √8 isn’t fully simplified, and other forms like 4√2 or √2 aren’t equal to √8 or its simplified version (4√2 would be much larger, and √2 is too small).

The main idea is to pull out any square factors from under the square root. For √8, find a perfect square that divides 8. Since 8 = 4 × 2 and 4 is a perfect square, you can rewrite the radical as √(4×2) = √4 × √2 = 2 × √2 = 2√2. This is the simplest form because there are no more perfect-square factors inside the radical.

Leaving it as √8 isn’t fully simplified, and other forms like 4√2 or √2 aren’t equal to √8 or its simplified version (4√2 would be much larger, and √2 is too small).