Answer :
Sure! Let's simplify the expression [tex]\(\sqrt{\frac{12}{25}}\)[/tex] step-by-step.
1. Start with the expression:
[tex]\[
\sqrt{\frac{12}{25}}
\][/tex]
2. Simplify inside the square root:
The fraction [tex]\(\frac{12}{25}\)[/tex] can be expressed as [tex]\(\frac{4 \times 3}{5 \times 5}\)[/tex].
3. Separate the square root for the numerator and the denominator:
[tex]\[
\sqrt{\frac{12}{25}} = \frac{\sqrt{12}}{\sqrt{25}}
\][/tex]
4. Simplify [tex]\(\sqrt{12}\)[/tex]:
[tex]\(\sqrt{12}\)[/tex] can be broken down as [tex]\(\sqrt{4 \times 3}\)[/tex], which equals [tex]\(\sqrt{4} \times \sqrt{3}\)[/tex].
5. Calculate the square roots:
- [tex]\(\sqrt{4} = 2\)[/tex]
- [tex]\(\sqrt{3}\)[/tex] remains as it is since it's an irrational number.
So, [tex]\(\sqrt{12} = 2 \times \sqrt{3} = 2\sqrt{3}\)[/tex].
6. Simplify [tex]\(\sqrt{25}\)[/tex]:
[tex]\(\sqrt{25} = 5\)[/tex].
7. Put it all together:
[tex]\[
\frac{\sqrt{12}}{\sqrt{25}} = \frac{2\sqrt{3}}{5}
\][/tex]
Therefore, the simplified form of [tex]\(\sqrt{\frac{12}{25}}\)[/tex] is [tex]\(\frac{2\sqrt{3}}{5}\)[/tex].
1. Start with the expression:
[tex]\[
\sqrt{\frac{12}{25}}
\][/tex]
2. Simplify inside the square root:
The fraction [tex]\(\frac{12}{25}\)[/tex] can be expressed as [tex]\(\frac{4 \times 3}{5 \times 5}\)[/tex].
3. Separate the square root for the numerator and the denominator:
[tex]\[
\sqrt{\frac{12}{25}} = \frac{\sqrt{12}}{\sqrt{25}}
\][/tex]
4. Simplify [tex]\(\sqrt{12}\)[/tex]:
[tex]\(\sqrt{12}\)[/tex] can be broken down as [tex]\(\sqrt{4 \times 3}\)[/tex], which equals [tex]\(\sqrt{4} \times \sqrt{3}\)[/tex].
5. Calculate the square roots:
- [tex]\(\sqrt{4} = 2\)[/tex]
- [tex]\(\sqrt{3}\)[/tex] remains as it is since it's an irrational number.
So, [tex]\(\sqrt{12} = 2 \times \sqrt{3} = 2\sqrt{3}\)[/tex].
6. Simplify [tex]\(\sqrt{25}\)[/tex]:
[tex]\(\sqrt{25} = 5\)[/tex].
7. Put it all together:
[tex]\[
\frac{\sqrt{12}}{\sqrt{25}} = \frac{2\sqrt{3}}{5}
\][/tex]
Therefore, the simplified form of [tex]\(\sqrt{\frac{12}{25}}\)[/tex] is [tex]\(\frac{2\sqrt{3}}{5}\)[/tex].