College Math Placement Practice Test

What is the simplified form of the radical √(50)?

1. √25

2. 5√5

3. 5√2

4. 10

The correct answer is: 5√2

To simplify the radical √(50), we begin by breaking down the number under the square root into its prime factors. The number 50 can be expressed as: \[ 50 = 25 \times 2 \] Since 25 is a perfect square (specifically, \( 5^2 \)), we can rewrite the square root: \[ \sqrt{50} = \sqrt{25 \times 2} \] Using the property of square roots that states \( \sqrt{a \times b} = \sqrt{a} \times \sqrt{b} \), we can separate the square root: \[ \sqrt{50} = \sqrt{25} \times \sqrt{2} \] Since \( \sqrt{25} = 5 \), we substitute that value back in: \[ \sqrt{50} = 5 \times \sqrt{2} \] Thus, the simplified form of √(50) is \( 5\sqrt{2} \), which corresponds to the correct answer. In this case, the other options do not accurately represent the simplification of √(50).