Answer :
To simplify [tex]\(\sqrt{\frac{12}{25}}\)[/tex], we should follow these steps:
1. Work with the Fraction Inside the Square Root:
- The expression inside the square root is [tex]\(\frac{12}{25}\)[/tex].
2. Split the Square Root Over the Numerator and Denominator:
- We can break down the square root of a fraction into the square root of its numerator and the square root of its denominator:
[tex]\[
\sqrt{\frac{12}{25}} = \frac{\sqrt{12}}{\sqrt{25}}
\][/tex]
3. Simplify the Denominator:
- The square root of the denominator, [tex]\(\sqrt{25}\)[/tex], is straightforward:
[tex]\[
\sqrt{25} = 5
\][/tex]
4. Simplify the Numerator:
- To simplify the numerator [tex]\(\sqrt{12}\)[/tex], notice that 12 can be factored into [tex]\(4 \times 3\)[/tex].
- This means:
[tex]\[
\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}
\][/tex]
5. Combine Results:
- Substitute back into the split fraction:
[tex]\[
\sqrt{\frac{12}{25}} = \frac{2\sqrt{3}}{5}
\][/tex]
6. Approximate Numerically:
- Using numerical calculation (e.g., with a calculator), you find that [tex]\(\frac{2\sqrt{3}}{5}\)[/tex] approximately equals 0.6928.
Therefore, the simplified form of [tex]\(\sqrt{\frac{12}{25}}\)[/tex] is [tex]\(\frac{2\sqrt{3}}{5}\)[/tex] which is approximately equal to 0.6928 when evaluated numerically.
1. Work with the Fraction Inside the Square Root:
- The expression inside the square root is [tex]\(\frac{12}{25}\)[/tex].
2. Split the Square Root Over the Numerator and Denominator:
- We can break down the square root of a fraction into the square root of its numerator and the square root of its denominator:
[tex]\[
\sqrt{\frac{12}{25}} = \frac{\sqrt{12}}{\sqrt{25}}
\][/tex]
3. Simplify the Denominator:
- The square root of the denominator, [tex]\(\sqrt{25}\)[/tex], is straightforward:
[tex]\[
\sqrt{25} = 5
\][/tex]
4. Simplify the Numerator:
- To simplify the numerator [tex]\(\sqrt{12}\)[/tex], notice that 12 can be factored into [tex]\(4 \times 3\)[/tex].
- This means:
[tex]\[
\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}
\][/tex]
5. Combine Results:
- Substitute back into the split fraction:
[tex]\[
\sqrt{\frac{12}{25}} = \frac{2\sqrt{3}}{5}
\][/tex]
6. Approximate Numerically:
- Using numerical calculation (e.g., with a calculator), you find that [tex]\(\frac{2\sqrt{3}}{5}\)[/tex] approximately equals 0.6928.
Therefore, the simplified form of [tex]\(\sqrt{\frac{12}{25}}\)[/tex] is [tex]\(\frac{2\sqrt{3}}{5}\)[/tex] which is approximately equal to 0.6928 when evaluated numerically.