Answer :
To simplify [tex]\(\sqrt{\frac{12}{25}}\)[/tex], let's follow these steps:
1. Notice the Expression:
The expression is a square root of a fraction: [tex]\(\sqrt{\frac{12}{25}}\)[/tex].
2. Apply the Property of Square Roots:
We can use the property [tex]\(\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}\)[/tex]. This means we can separate the square root of a fraction into the square root of the numerator and the square root of the denominator.
3. Simplify Each Part:
- Numerator: [tex]\(\sqrt{12} \approx 3.4641\)[/tex]
- Denominator: [tex]\(\sqrt{25} = 5\)[/tex]
4. Divide the Simplified Parts:
Now, divide the square root of the numerator by the square root of the denominator:
[tex]\[
\frac{\sqrt{12}}{\sqrt{25}} = \frac{3.4641}{5} \approx 0.6928
\][/tex]
Therefore, [tex]\(\sqrt{\frac{12}{25}} \approx 0.6928\)[/tex].
1. Notice the Expression:
The expression is a square root of a fraction: [tex]\(\sqrt{\frac{12}{25}}\)[/tex].
2. Apply the Property of Square Roots:
We can use the property [tex]\(\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}\)[/tex]. This means we can separate the square root of a fraction into the square root of the numerator and the square root of the denominator.
3. Simplify Each Part:
- Numerator: [tex]\(\sqrt{12} \approx 3.4641\)[/tex]
- Denominator: [tex]\(\sqrt{25} = 5\)[/tex]
4. Divide the Simplified Parts:
Now, divide the square root of the numerator by the square root of the denominator:
[tex]\[
\frac{\sqrt{12}}{\sqrt{25}} = \frac{3.4641}{5} \approx 0.6928
\][/tex]
Therefore, [tex]\(\sqrt{\frac{12}{25}} \approx 0.6928\)[/tex].