Solve sqrt{2.58^2/1000+left(2.50right)^2/1200}

$$\sqrt{ \frac{ { 2.58 }^{ 2 } }{ 1000 } + \frac{ { \left(2.50 \right) }^{ 2 } }{ 1200 } }$$

Evaluate

$$\frac{\sqrt{2669565}}{15000}\approx 0.108925357$$

Solution Steps

Calculate 2.58 to the power of 2 and get 6.6564.

$$\sqrt{\frac{6.6564}{1000}+\frac{2.5^{2}}{1200}}$$

Expand \frac{6.6564}{1000} by multiplying both numerator and the denominator by 10000.

$$\sqrt{\frac{66564}{10000000}+\frac{2.5^{2}}{1200}}$$

Reduce the fraction \frac{66564}{10000000} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{16641}{2500000}+\frac{2.5^{2}}{1200}}$$

Calculate 2.5 to the power of 2 and get 6.25.

$$\sqrt{\frac{16641}{2500000}+\frac{6.25}{1200}}$$

Expand \frac{6.25}{1200} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{16641}{2500000}+\frac{625}{120000}}$$

Reduce the fraction \frac{625}{120000} to lowest terms by extracting and canceling out 625.

$$\sqrt{\frac{16641}{2500000}+\frac{1}{192}}$$

Least common multiple of 2500000 and 192 is 15000000. Convert \frac{16641}{2500000} and \frac{1}{192} to fractions with denominator 15000000.

$$\sqrt{\frac{99846}{15000000}+\frac{78125}{15000000}}$$

Since \frac{99846}{15000000} and \frac{78125}{15000000} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{99846+78125}{15000000}}$$

Add 99846 and 78125 to get 177971.

$$\sqrt{\frac{177971}{15000000}}$$

Rewrite the square root of the division \sqrt{\frac{177971}{15000000}} as the division of square roots \frac{\sqrt{177971}}{\sqrt{15000000}}.

$$\frac{\sqrt{177971}}{\sqrt{15000000}}$$

Factor 15000000=1000^{2}\times 15. Rewrite the square root of the product \sqrt{1000^{2}\times 15} as the product of square roots \sqrt{1000^{2}}\sqrt{15}. Take the square root of 1000^{2}.

$$\frac{\sqrt{177971}}{1000\sqrt{15}}$$

Rationalize the denominator of \frac{\sqrt{177971}}{1000\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

$$\frac{\sqrt{177971}\sqrt{15}}{1000\left(\sqrt{15}\right)^{2}}$$

The square of \sqrt{15} is 15.

$$\frac{\sqrt{177971}\sqrt{15}}{1000\times 15}$$

To multiply \sqrt{177971} and \sqrt{15}, multiply the numbers under the square root.

$$\frac{\sqrt{2669565}}{1000\times 15}$$

Multiply 1000 and 15 to get 15000.

$$\frac{\sqrt{2669565}}{15000}$$