Solve {left(26.sqrt{25./81538}right)}^2

$${ \left(26. \sqrt{ \frac{ 25. }{ 81538 } } \right) }^{ 2 }$$

Evaluate

$$\frac{8450}{40769}\approx 0.207265324$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{25}{81538}} as the division of square roots \frac{\sqrt{25}}{\sqrt{81538}}.

$$\left(26\times \frac{\sqrt{25}}{\sqrt{81538}}\right)^{2}$$

Calculate the square root of 25 and get 5.

$$\left(26\times \frac{5}{\sqrt{81538}}\right)^{2}$$

Rationalize the denominator of \frac{5}{\sqrt{81538}} by multiplying numerator and denominator by \sqrt{81538}.

$$\left(26\times \frac{5\sqrt{81538}}{\left(\sqrt{81538}\right)^{2}}\right)^{2}$$

The square of \sqrt{81538} is 81538.

$$\left(26\times \frac{5\sqrt{81538}}{81538}\right)^{2}$$

Express 26\times \frac{5\sqrt{81538}}{81538} as a single fraction.

$$\left(\frac{26\times 5\sqrt{81538}}{81538}\right)^{2}$$

To raise \frac{26\times 5\sqrt{81538}}{81538} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(26\times 5\sqrt{81538}\right)^{2}}{81538^{2}}$$

Multiply 26 and 5 to get 130.

$$\frac{\left(130\sqrt{81538}\right)^{2}}{81538^{2}}$$

Expand \left(130\sqrt{81538}\right)^{2}.

$$\frac{130^{2}\left(\sqrt{81538}\right)^{2}}{81538^{2}}$$

Calculate 130 to the power of 2 and get 16900.

$$\frac{16900\left(\sqrt{81538}\right)^{2}}{81538^{2}}$$

The square of \sqrt{81538} is 81538.

$$\frac{16900\times 81538}{81538^{2}}$$

Multiply 16900 and 81538 to get 1377992200.

$$\frac{1377992200}{81538^{2}}$$

Calculate 81538 to the power of 2 and get 6648445444.

$$\frac{1377992200}{6648445444}$$

Reduce the fraction \frac{1377992200}{6648445444} to lowest terms by extracting and canceling out 163076.

$$\frac{8450}{40769}$$

Factor

$$\frac{2 \cdot 5 ^ {2} \cdot 13 ^ {2}}{59 \cdot 691} = 0.2072653241433442$$