Let's simplify the expression [tex]\(\sqrt{50}\)[/tex] step-by-step:
1. Factorize the number under the square root:
We start by expressing 50 as a product of its prime factors. The number 50 can be factorized as:
[tex]\[
50 = 2 \times 25
\][/tex]
Notice that 25 is a perfect square, so we can further factorize it:
[tex]\[
25 = 5 \times 5
\][/tex]
Therefore:
[tex]\[
50 = 2 \times 5^2
\][/tex]
2. Apply the square root to the product:
Using the property of square roots [tex]\(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\)[/tex], we can separate the factors under the square root:
[tex]\[
\sqrt{50} = \sqrt{2 \times 5^2} = \sqrt{2} \times \sqrt{5^2}
\][/tex]
3. Simplify the square root of the perfect square:
Since the square root of [tex]\(5^2\)[/tex] is 5, we have:
[tex]\[
\sqrt{5^2} = 5
\][/tex]
Therefore, we can simplify our expression:
[tex]\[
\sqrt{50} = \sqrt{2} \times 5
\][/tex]
4. Write the simplified expression:
Putting it all together, we get:
[tex]\[
\sqrt{50} = 5\sqrt{2}
\][/tex]
So, the simplified form of [tex]\(\sqrt{50}\)[/tex] is:
[tex]\[
5\sqrt{2}
\][/tex]
