To find the simplest rationalizing factor of [tex]\(\sqrt{50}\)[/tex], follow these steps:
1. Simplify the expression inside the square root:
[tex]\(\sqrt{50}\)[/tex] can be broken down as [tex]\(\sqrt{25 \times 2}\)[/tex].
2. Use the property of square roots to simplify:
[tex]\(\sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2}\)[/tex].
3. Evaluate the square root of 25:
[tex]\(\sqrt{25} = 5\)[/tex].
4. Combine the simplified parts:
Therefore, [tex]\(\sqrt{50} = 5 \sqrt{2}\)[/tex].
Now, to rationalize an expression involving a square root, the rationalizing factor is typically the simplest form that makes the expression a rational number.
Since we have [tex]\(\sqrt{50} = 5 \sqrt{2}\)[/tex], to rationalize this expression, we should consider the factor involving the remaining square root.
5. Identify the remaining square root:
The remaining square root in the expression [tex]\(5 \sqrt{2}\)[/tex] is [tex]\(\sqrt{2}\)[/tex].
6. Determine the simplest form of the rationalizing factor:
The simplest rationalizing factor for [tex]\(\sqrt{50}\)[/tex] is thus [tex]\(\sqrt{2}\)[/tex].
Therefore, the simplest rationalizing factor of [tex]\(\sqrt{50}\)[/tex] is [tex]\(\sqrt{2}\)[/tex]. The numerical value of [tex]\(\sqrt{2}\)[/tex] is approximately [tex]\(1.4142135623730951\)[/tex].
