What is the simplified form of √50?

• A. 5√1
• B. 5√2
• C. 10√2
• D. 25√2

Answer: (B)

To simplify the square root of 50, we start by factoring 50 into its prime factors. The number 50 can be expressed as 25 times 2, since ( 25 \times 2 = 50 ).

Next, we know that the square root of a product can be separated into the product of the square roots of the factors:

[

\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2}

]

Here, the square root of 25 is 5, as 5 times 5 equals 25. Therefore, we can substitute this back into our equation:

[

\sqrt{50} = 5 \times \sqrt{2}

]

This gives us the simplified form of ( \sqrt{50} ) as ( 5\sqrt{2} ).

Understanding how to factor numbers and apply the property of square roots is essential in reaching the correct answer. This process highlights the importance of recognizing perfect squares and how they can simplify square root calculations, enabling students to work through similar problems effectively in the future.