Solve sqrt{frac{5^2/7^2}}{5*3204}*222528+62555

$$\frac{ \sqrt{ \frac{ { 5 }^{ 2 } }{ { 7 }^{ 2 } } } }{ 5 \cdot 3204 } \times 222528+62555$$

Evaluate

$$\frac{116933839}{1869}\approx 62564.92188336$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$222528\times \frac{\sqrt{\frac{25}{7^{2}}}}{5\times 3204}+62555$$

Calculate 7 to the power of 2 and get 49.

$$222528\times \frac{\sqrt{\frac{25}{49}}}{5\times 3204}+62555$$

Rewrite the square root of the division \frac{25}{49} as the division of square roots \frac{\sqrt{25}}{\sqrt{49}}. Take the square root of both numerator and denominator.

$$222528\times \frac{\frac{5}{7}}{5\times 3204}+62555$$

Multiply 5 and 3204 to get 16020.

$$222528\times \frac{\frac{5}{7}}{16020}+62555$$

Express \frac{\frac{5}{7}}{16020} as a single fraction.

$$222528\times \frac{5}{7\times 16020}+62555$$

Multiply 7 and 16020 to get 112140.

$$222528\times \frac{5}{112140}+62555$$

Reduce the fraction \frac{5}{112140} to lowest terms by extracting and canceling out 5.

$$222528\times \frac{1}{22428}+62555$$

Multiply 222528 and \frac{1}{22428} to get \frac{222528}{22428}.

$$\frac{222528}{22428}+62555$$

Reduce the fraction \frac{222528}{22428} to lowest terms by extracting and canceling out 12.

$$\frac{18544}{1869}+62555$$

Convert 62555 to fraction \frac{116915295}{1869}.

$$\frac{18544}{1869}+\frac{116915295}{1869}$$

Since \frac{18544}{1869} and \frac{116915295}{1869} have the same denominator, add them by adding their numerators.

$$\frac{18544+116915295}{1869}$$

Add 18544 and 116915295 to get 116933839.

$$\frac{116933839}{1869}$$

Factor

$$\frac{11 \cdot 359 \cdot 29611}{3 \cdot 7 \cdot 89} = 62564\frac{1723}{1869} = 62564.92188336008$$