Solve sqrt{5/66^45}

$$\sqrt{ \frac{ 5 }{ { 66 }^{ 45 } } }$$

Evaluate

$$\frac{\sqrt{330}}{707148325734900438472232667507267307831296}\approx 2.568895586 \cdot 10^{-41}$$

Solution Steps

Calculate 66 to the power of 45 and get 7576647796813225056892249002163209647292766903576209054405786574049618426830258176.

$$\sqrt{\frac{5}{7576647796813225056892249002163209647292766903576209054405786574049618426830258176}}$$

Rewrite the square root of the division \sqrt{\frac{5}{7576647796813225056892249002163209647292766903576209054405786574049618426830258176}} as the division of square roots \frac{\sqrt{5}}{\sqrt{7576647796813225056892249002163209647292766903576209054405786574049618426830258176}}.

$$\frac{\sqrt{5}}{\sqrt{7576647796813225056892249002163209647292766903576209054405786574049618426830258176}}$$

Factor 7576647796813225056892249002163209647292766903576209054405786574049618426830258176=10714368571740915734427767689504050118656^{2}\times 66. Rewrite the square root of the product \sqrt{10714368571740915734427767689504050118656^{2}\times 66} as the product of square roots \sqrt{10714368571740915734427767689504050118656^{2}}\sqrt{66}. Take the square root of 10714368571740915734427767689504050118656^{2}.

$$\frac{\sqrt{5}}{10714368571740915734427767689504050118656\sqrt{66}}$$

Rationalize the denominator of \frac{\sqrt{5}}{10714368571740915734427767689504050118656\sqrt{66}} by multiplying numerator and denominator by \sqrt{66}.

$$\frac{\sqrt{5}\sqrt{66}}{10714368571740915734427767689504050118656\left(\sqrt{66}\right)^{2}}$$

The square of \sqrt{66} is 66.

$$\frac{\sqrt{5}\sqrt{66}}{10714368571740915734427767689504050118656\times 66}$$

To multiply \sqrt{5} and \sqrt{66}, multiply the numbers under the square root.

$$\frac{\sqrt{330}}{10714368571740915734427767689504050118656\times 66}$$

Multiply 10714368571740915734427767689504050118656 and 66 to get 707148325734900438472232667507267307831296.

$$\frac{\sqrt{330}}{707148325734900438472232667507267307831296}$$