Simplify \(\sqrt{\frac{49}{144}}\) to \(\frac{\sqrt{49}}{\sqrt{144}}\).
\[\sqrt{\frac{25}{64}+\frac{\sqrt{49}}{\sqrt{144}}}\]
Since \(7\times 7=49\), the square root of \(49\) is \(7\).
\[\sqrt{\frac{25}{64}+\frac{7}{\sqrt{144}}}\]
Since \(12\times 12=144\), the square root of \(144\) is \(12\).
\[\sqrt{\frac{25}{64}+\frac{7}{12}}\]
Simplify \(\frac{25}{64}+\frac{7}{12}\) to \(\frac{187}{192}\).
\[\sqrt{\frac{187}{192}}\]
Simplify.
\[\frac{\sqrt{187}}{\sqrt{192}}\]
Simplify \(\sqrt{192}\) to \(8\sqrt{3}\).
\[\frac{\sqrt{187}}{8\sqrt{3}}\]
Rationalize the denominator: \(\frac{\sqrt{187}}{8\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}=\frac{\sqrt{187}\sqrt{3}}{8\times 3}\).
\[\frac{\sqrt{187}\sqrt{3}}{8\times 3}\]
Simplify \(\sqrt{187}\sqrt{3}\) to \(\sqrt{561}\).
\[\frac{\sqrt{561}}{8\times 3}\]
Simplify \(8\times 3\) to \(24\).
\[\frac{\sqrt{561}}{24}\]
Decimal Form: 0.986893
sqrt(561)/24
