Which is the simplified form of sqrt(50)?

Which is the simplified form of sqrt(50)?

• A. √50
• B. 5√5
• C. 10√2
• D. 5√2

Answer: (D)

When simplifying a square root, you pull out any perfect square factors from under the radical. Here, 50 can be written as 25 × 2, and 25 is a perfect square. So the square root splits: sqrt(50) = sqrt(25) × sqrt(2) = 5 × sqrt(2) = 5√2. This is the simplest form because 2 has no square factors besides 1. Leaving it as √50 isn’t fully simplified. A form like 5√5 would come from rewriting 50 as 25×5, which doesn’t match the original radicand. And 10√2 would imply the radicand is 200, not 50, so it isn’t equivalent to sqrt(50).

When simplifying a square root, you pull out any perfect square factors from under the radical. Here, 50 can be written as 25 × 2, and 25 is a perfect square. So the square root splits: sqrt(50) = sqrt(25) × sqrt(2) = 5 × sqrt(2) = 5√2. This is the simplest form because 2 has no square factors besides 1.

Leaving it as √50 isn’t fully simplified. A form like 5√5 would come from rewriting 50 as 25×5, which doesn’t match the original radicand. And 10√2 would imply the radicand is 200, not 50, so it isn’t equivalent to sqrt(50).