Solve sqrt{510.4^2/90}

$$\sqrt{ \frac{ { 510.4 }^{ 2 } }{ 90 } }$$

Evaluate

$$\frac{1276\sqrt{10}}{75}\approx 53.800883925$$

Solution Steps

Calculate 510.4 to the power of 2 and get 260508.16.

$$\sqrt{\frac{260508.16}{90}}$$

Expand \frac{260508.16}{90} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{26050816}{9000}}$$

Reduce the fraction \frac{26050816}{9000} to lowest terms by extracting and canceling out 8.

$$\sqrt{\frac{3256352}{1125}}$$

Rewrite the square root of the division \sqrt{\frac{3256352}{1125}} as the division of square roots \frac{\sqrt{3256352}}{\sqrt{1125}}.

$$\frac{\sqrt{3256352}}{\sqrt{1125}}$$

Factor 3256352=1276^{2}\times 2. Rewrite the square root of the product \sqrt{1276^{2}\times 2} as the product of square roots \sqrt{1276^{2}}\sqrt{2}. Take the square root of 1276^{2}.

$$\frac{1276\sqrt{2}}{\sqrt{1125}}$$

Factor 1125=15^{2}\times 5. Rewrite the square root of the product \sqrt{15^{2}\times 5} as the product of square roots \sqrt{15^{2}}\sqrt{5}. Take the square root of 15^{2}.

$$\frac{1276\sqrt{2}}{15\sqrt{5}}$$

Rationalize the denominator of \frac{1276\sqrt{2}}{15\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{1276\sqrt{2}\sqrt{5}}{15\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{1276\sqrt{2}\sqrt{5}}{15\times 5}$$

To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{1276\sqrt{10}}{15\times 5}$$

Multiply 15 and 5 to get 75.

$$\frac{1276\sqrt{10}}{75}$$