Solve 6280sqrt{frac{9/10+785^2}}{9984^2+10*785^2}

$$\frac{ 6280 \sqrt{ \frac{ 9 }{ 10 } + { 785 }^{ 2 } } }{ 9 { 984 }^{ 2 } +10 \times { 785 }^{ 2 } }$$

Evaluate

$$\frac{314\sqrt{61622590}}{7438277}\approx 0.331380749$$

Solution Steps

Calculate 785 to the power of 2 and get 616225.

$$\frac{6280\sqrt{\frac{9}{10}+616225}}{9\times 984^{2}+10\times 785^{2}}$$

Convert 616225 to fraction \frac{6162250}{10}.

$$\frac{6280\sqrt{\frac{9}{10}+\frac{6162250}{10}}}{9\times 984^{2}+10\times 785^{2}}$$

Since \frac{9}{10} and \frac{6162250}{10} have the same denominator, add them by adding their numerators.

$$\frac{6280\sqrt{\frac{9+6162250}{10}}}{9\times 984^{2}+10\times 785^{2}}$$

Add 9 and 6162250 to get 6162259.

$$\frac{6280\sqrt{\frac{6162259}{10}}}{9\times 984^{2}+10\times 785^{2}}$$

Rewrite the square root of the division \sqrt{\frac{6162259}{10}} as the division of square roots \frac{\sqrt{6162259}}{\sqrt{10}}.

$$\frac{6280\times \frac{\sqrt{6162259}}{\sqrt{10}}}{9\times 984^{2}+10\times 785^{2}}$$

Rationalize the denominator of \frac{\sqrt{6162259}}{\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{6280\times \frac{\sqrt{6162259}\sqrt{10}}{\left(\sqrt{10}\right)^{2}}}{9\times 984^{2}+10\times 785^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{6280\times \frac{\sqrt{6162259}\sqrt{10}}{10}}{9\times 984^{2}+10\times 785^{2}}$$

To multiply \sqrt{6162259} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{6280\times \frac{\sqrt{61622590}}{10}}{9\times 984^{2}+10\times 785^{2}}$$

Cancel out 10, the greatest common factor in 6280 and 10.

$$\frac{628\sqrt{61622590}}{9\times 984^{2}+10\times 785^{2}}$$

Calculate 984 to the power of 2 and get 968256.

$$\frac{628\sqrt{61622590}}{9\times 968256+10\times 785^{2}}$$

Multiply 9 and 968256 to get 8714304.

$$\frac{628\sqrt{61622590}}{8714304+10\times 785^{2}}$$

Calculate 785 to the power of 2 and get 616225.

$$\frac{628\sqrt{61622590}}{8714304+10\times 616225}$$

Multiply 10 and 616225 to get 6162250.

$$\frac{628\sqrt{61622590}}{8714304+6162250}$$

Add 8714304 and 6162250 to get 14876554.

$$\frac{628\sqrt{61622590}}{14876554}$$

Divide 628\sqrt{61622590} by 14876554 to get \frac{314}{7438277}\sqrt{61622590}.

$$\frac{314}{7438277}\sqrt{61622590}$$