Fully simplify in radical form: [tex]\(\sqrt{50}\)[/tex]

A. [tex]\(5 \sqrt{10}\)[/tex]

B. [tex]\(10 \sqrt{5}\)[/tex]

C. 7.07

D. [tex]\(5 \sqrt{2}\)[/tex]



Answer :

To simplify the radical [tex]\(\sqrt{50}\)[/tex], we start by breaking down 50 into its prime factors.

The number 50 can be factored as [tex]\(50 = 25 \times 2\)[/tex]. Notice that 25 is a perfect square. We can then rewrite the square root of 50 using these factors:

[tex]\[ \sqrt{50} = \sqrt{25 \times 2} \][/tex]

Using the property of square roots that allows us to separate the factors, we have:

[tex]\[ \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} \][/tex]

Since [tex]\(\sqrt{25}\)[/tex] is 5 (because [tex]\(5^2 = 25\)[/tex]), we can simplify further:

[tex]\[ \sqrt{25} \times \sqrt{2} = 5 \sqrt{2} \][/tex]

Therefore, the simplified form of [tex]\(\sqrt{50}\)[/tex] is:

[tex]\[ 5 \sqrt{2} \][/tex]

The correct answer from the given choices is:

D. [tex]\(5 \sqrt{2}\)[/tex]

For verification, converting [tex]\(5 \sqrt{2}\)[/tex] to a numerical form, we get approximately 7.0710678118654755. This confirms that our simplified radical form is correct.