Solve sqrt{667*10^-11598*10^24/900+6378}

$$\sqrt{ \frac{ 667 \times { 10 }^{ -11 } 598 \times { 10 }^{ 24 } }{ 900+6378 } }$$

Evaluate

$$\frac{23000000\sqrt{13719030}}{3639}\approx 23410327.17673061$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -11 and 24 to get 13.

$$\sqrt{\frac{667\times 10^{13}\times 598}{900+6378}}$$

Calculate 10 to the power of 13 and get 10000000000000.

$$\sqrt{\frac{667\times 10000000000000\times 598}{900+6378}}$$

Multiply 667 and 10000000000000 to get 6670000000000000.

$$\sqrt{\frac{6670000000000000\times 598}{900+6378}}$$

Multiply 6670000000000000 and 598 to get 3988660000000000000.

$$\sqrt{\frac{3988660000000000000}{900+6378}}$$

Add 900 and 6378 to get 7278.

$$\sqrt{\frac{3988660000000000000}{7278}}$$

Reduce the fraction \frac{3988660000000000000}{7278} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{1994330000000000000}{3639}}$$

Rewrite the square root of the division \sqrt{\frac{1994330000000000000}{3639}} as the division of square roots \frac{\sqrt{1994330000000000000}}{\sqrt{3639}}.

$$\frac{\sqrt{1994330000000000000}}{\sqrt{3639}}$$

Factor 1994330000000000000=23000000^{2}\times 3770. Rewrite the square root of the product \sqrt{23000000^{2}\times 3770} as the product of square roots \sqrt{23000000^{2}}\sqrt{3770}. Take the square root of 23000000^{2}.

$$\frac{23000000\sqrt{3770}}{\sqrt{3639}}$$

Rationalize the denominator of \frac{23000000\sqrt{3770}}{\sqrt{3639}} by multiplying numerator and denominator by \sqrt{3639}.

$$\frac{23000000\sqrt{3770}\sqrt{3639}}{\left(\sqrt{3639}\right)^{2}}$$

The square of \sqrt{3639} is 3639.

$$\frac{23000000\sqrt{3770}\sqrt{3639}}{3639}$$

To multiply \sqrt{3770} and \sqrt{3639}, multiply the numbers under the square root.

$$\frac{23000000\sqrt{13719030}}{3639}$$