Solve sqrt{2*6.673*10^-11*4*6*10^24/6400+35780}

$$\sqrt { \frac { 2 \times 6.673 \times 10 ^ { - 11 } \times 4 \times 6 \times 10 ^ { 24 } } { 6400 + 35780 } }$$

Evaluate

$$\frac{40000\sqrt{23455595}}{703}\approx 275567.434751107$$

Solution Steps

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

$$\sqrt{\frac{2\times 6.673\times 10^{13}\times 4\times 6}{6400+35780}}$$

Multiply 2 and 6.673 to get 13.346.

$$\sqrt{\frac{13.346\times 10^{13}\times 4\times 6}{6400+35780}}$$

Calculate 10 to the power of 13 and get 10000000000000.

$$\sqrt{\frac{13.346\times 10000000000000\times 4\times 6}{6400+35780}}$$

Multiply 13.346 and 10000000000000 to get 133460000000000.

$$\sqrt{\frac{133460000000000\times 4\times 6}{6400+35780}}$$

Multiply 133460000000000 and 4 to get 533840000000000.

$$\sqrt{\frac{533840000000000\times 6}{6400+35780}}$$

Multiply 533840000000000 and 6 to get 3203040000000000.

$$\sqrt{\frac{3203040000000000}{6400+35780}}$$

Add 6400 and 35780 to get 42180.

$$\sqrt{\frac{3203040000000000}{42180}}$$

Reduce the fraction \frac{3203040000000000}{42180} to lowest terms by extracting and canceling out 60.

$$\sqrt{\frac{53384000000000}{703}}$$

Rewrite the square root of the division \sqrt{\frac{53384000000000}{703}} as the division of square roots \frac{\sqrt{53384000000000}}{\sqrt{703}}.

$$\frac{\sqrt{53384000000000}}{\sqrt{703}}$$

Factor 53384000000000=40000^{2}\times 33365. Rewrite the square root of the product \sqrt{40000^{2}\times 33365} as the product of square roots \sqrt{40000^{2}}\sqrt{33365}. Take the square root of 40000^{2}.

$$\frac{40000\sqrt{33365}}{\sqrt{703}}$$

Rationalize the denominator of \frac{40000\sqrt{33365}}{\sqrt{703}} by multiplying numerator and denominator by \sqrt{703}.

$$\frac{40000\sqrt{33365}\sqrt{703}}{\left(\sqrt{703}\right)^{2}}$$

The square of \sqrt{703} is 703.

$$\frac{40000\sqrt{33365}\sqrt{703}}{703}$$

To multiply \sqrt{33365} and \sqrt{703}, multiply the numbers under the square root.

$$\frac{40000\sqrt{23455595}}{703}$$