Solve sqrt{6250000000000-15625000000div6.64}

$$\sqrt{ 6250000000000-15625000000 \div 6.64 }$$

Evaluate

$$\frac{937500\sqrt{48970}}{83}\approx 2499529.323162542$$

Solution Steps

Expand \frac{15625000000}{6.64} by multiplying both numerator and the denominator by 100.

$$\sqrt{6250000000000-\frac{1562500000000}{664}}$$

Reduce the fraction \frac{1562500000000}{664} to lowest terms by extracting and canceling out 8.

$$\sqrt{6250000000000-\frac{195312500000}{83}}$$

Convert 6250000000000 to fraction \frac{518750000000000}{83}.

$$\sqrt{\frac{518750000000000}{83}-\frac{195312500000}{83}}$$

Since \frac{518750000000000}{83} and \frac{195312500000}{83} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{518750000000000-195312500000}{83}}$$

Subtract 195312500000 from 518750000000000 to get 518554687500000.

$$\sqrt{\frac{518554687500000}{83}}$$

Rewrite the square root of the division \sqrt{\frac{518554687500000}{83}} as the division of square roots \frac{\sqrt{518554687500000}}{\sqrt{83}}.

$$\frac{\sqrt{518554687500000}}{\sqrt{83}}$$

Factor 518554687500000=937500^{2}\times 590. Rewrite the square root of the product \sqrt{937500^{2}\times 590} as the product of square roots \sqrt{937500^{2}}\sqrt{590}. Take the square root of 937500^{2}.

$$\frac{937500\sqrt{590}}{\sqrt{83}}$$

Rationalize the denominator of \frac{937500\sqrt{590}}{\sqrt{83}} by multiplying numerator and denominator by \sqrt{83}.

$$\frac{937500\sqrt{590}\sqrt{83}}{\left(\sqrt{83}\right)^{2}}$$

The square of \sqrt{83} is 83.

$$\frac{937500\sqrt{590}\sqrt{83}}{83}$$

To multiply \sqrt{590} and \sqrt{83}, multiply the numbers under the square root.

$$\frac{937500\sqrt{48970}}{83}$$