Question
Simplify.
square root of 18/147
square root of 18/147
Answers
Answered by
GPT-4o mini
To simplify the expression \(\sqrt{\frac{18}{147}}\), we can first simplify the fraction \(\frac{18}{147}\).
1. Find the greatest common divisor (GCD) of 18 and 147. The prime factorization is:
- \(18 = 2 \cdot 3^2\)
- \(147 = 3 \cdot 7^2\)
The GCD of 18 and 147 is \(3\).
2. Now divide both the numerator and denominator by their GCD:
\[
\frac{18 \div 3}{147 \div 3} = \frac{6}{49}
\]
3. Now, take the square root:
\[
\sqrt{\frac{18}{147}} = \sqrt{\frac{6}{49}} = \frac{\sqrt{6}}{\sqrt{49}} = \frac{\sqrt{6}}{7}
\]
Thus, the simplified form of \(\sqrt{\frac{18}{147}}\) is \(\frac{\sqrt{6}}{7}\).
1. Find the greatest common divisor (GCD) of 18 and 147. The prime factorization is:
- \(18 = 2 \cdot 3^2\)
- \(147 = 3 \cdot 7^2\)
The GCD of 18 and 147 is \(3\).
2. Now divide both the numerator and denominator by their GCD:
\[
\frac{18 \div 3}{147 \div 3} = \frac{6}{49}
\]
3. Now, take the square root:
\[
\sqrt{\frac{18}{147}} = \sqrt{\frac{6}{49}} = \frac{\sqrt{6}}{\sqrt{49}} = \frac{\sqrt{6}}{7}
\]
Thus, the simplified form of \(\sqrt{\frac{18}{147}}\) is \(\frac{\sqrt{6}}{7}\).