What is the simplified form of the square root of 50?

To simplify the square root of 50, you start by breaking it down into its prime factors. The number 50 can be expressed as ( 25 \times 2 ), where 25 is a perfect square.

The square root can then be simplified using the property that the square root of a product can be expressed as the product of the square roots of the factors. This gives us:

[

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

]

Since the square root of 25 is 5, we combine this with the square root of 2 to arrive at:

[

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

]

Thus, the simplified form of the square root of 50 is ( 5\sqrt{2} ). This form is often preferred because it expresses the result in terms of integers and simpler square roots. Other options, such as 5, 25, and 10, do not accurately represent the square root of 50 when simplified.