Solve sqrt{25*69+52/25^2}

$$\sqrt{ 25 \times 69+ \frac{ 52 }{ { 25 }^{ 2 } } }$$

Evaluate

$$\frac{\sqrt{1078177}}{25}\approx 41.534120913$$

Solution Steps

Multiply 25 and 69 to get 1725.

$$\sqrt{1725+\frac{52}{25^{2}}}$$

Calculate 25 to the power of 2 and get 625.

$$\sqrt{1725+\frac{52}{625}}$$

Convert 1725 to fraction \frac{1078125}{625}.

$$\sqrt{\frac{1078125}{625}+\frac{52}{625}}$$

Since \frac{1078125}{625} and \frac{52}{625} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{1078125+52}{625}}$$

Add 1078125 and 52 to get 1078177.

$$\sqrt{\frac{1078177}{625}}$$

Rewrite the square root of the division \sqrt{\frac{1078177}{625}} as the division of square roots \frac{\sqrt{1078177}}{\sqrt{625}}.

$$\frac{\sqrt{1078177}}{\sqrt{625}}$$

Calculate the square root of 625 and get 25.

$$\frac{\sqrt{1078177}}{25}$$