Solve 4sqrt{412/255}

$$4 \sqrt{ \frac{ 412 }{ 255 } }$$

Evaluate

$$\frac{8\sqrt{26265}}{255}\approx 5.084385941$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{412}{255}} as the division of square roots \frac{\sqrt{412}}{\sqrt{255}}.

$$4\times \frac{\sqrt{412}}{\sqrt{255}}$$

Factor 412=2^{2}\times 103. Rewrite the square root of the product \sqrt{2^{2}\times 103} as the product of square roots \sqrt{2^{2}}\sqrt{103}. Take the square root of 2^{2}.

$$4\times \frac{2\sqrt{103}}{\sqrt{255}}$$

Rationalize the denominator of \frac{2\sqrt{103}}{\sqrt{255}} by multiplying numerator and denominator by \sqrt{255}.

$$4\times \frac{2\sqrt{103}\sqrt{255}}{\left(\sqrt{255}\right)^{2}}$$

The square of \sqrt{255} is 255.

$$4\times \frac{2\sqrt{103}\sqrt{255}}{255}$$

To multiply \sqrt{103} and \sqrt{255}, multiply the numbers under the square root.

$$4\times \frac{2\sqrt{26265}}{255}$$

Express 4\times \frac{2\sqrt{26265}}{255} as a single fraction.

$$\frac{4\times 2\sqrt{26265}}{255}$$

Multiply 4 and 2 to get 8.

$$\frac{8\sqrt{26265}}{255}$$