Solve {left(1/{left(frac{180{345}right)}^2+{left(234/580right)}^2}right)}^frac{1{2}}

$${ \left( \frac{ 1 }{ { \left( \frac{ 180 }{ 345 } \right) }^{ 2 } + { \left( \frac{ 234 }{ 580 } \right) }^{ 2 } } \right) }^{ \frac{ 1 }{ 2 } }$$

Evaluate

$$\frac{6670\sqrt{2150209}}{6450627}\approx 1.516227054$$

Solution Steps

Reduce the fraction \frac{180}{345} to lowest terms by extracting and canceling out 15.

$$\left(\frac{1}{\left(\frac{12}{23}\right)^{2}+\left(\frac{234}{580}\right)^{2}}\right)^{\frac{1}{2}}$$

Calculate \frac{12}{23} to the power of 2 and get \frac{144}{529}.

$$\left(\frac{1}{\frac{144}{529}+\left(\frac{234}{580}\right)^{2}}\right)^{\frac{1}{2}}$$

Reduce the fraction \frac{234}{580} to lowest terms by extracting and canceling out 2.

$$\left(\frac{1}{\frac{144}{529}+\left(\frac{117}{290}\right)^{2}}\right)^{\frac{1}{2}}$$

Calculate \frac{117}{290} to the power of 2 and get \frac{13689}{84100}.

$$\left(\frac{1}{\frac{144}{529}+\frac{13689}{84100}}\right)^{\frac{1}{2}}$$

Add \frac{144}{529} and \frac{13689}{84100} to get \frac{19351881}{44488900}.

$$\left(\frac{1}{\frac{19351881}{44488900}}\right)^{\frac{1}{2}}$$

Divide 1 by \frac{19351881}{44488900} by multiplying 1 by the reciprocal of \frac{19351881}{44488900}.

$$\left(1\times \frac{44488900}{19351881}\right)^{\frac{1}{2}}$$

Multiply 1 and \frac{44488900}{19351881} to get \frac{44488900}{19351881}.

$$\left(\frac{44488900}{19351881}\right)^{\frac{1}{2}}$$