Solve sqrt{2.92114*10^36/2.96*10^-19}

$$\sqrt{ \frac{ 2.92114 \times { 10 }^{ 36 } }{ 2.96 \times { 10 }^{ -19 } } }$$

Evaluate

$$\frac{50000000000000000000000000\sqrt{5404109}}{37}\approx 3.141451291 \cdot 10^{27}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\sqrt{\frac{2.92114\times 10^{55}}{2.96}}$$

Calculate 10 to the power of 55 and get 10000000000000000000000000000000000000000000000000000000.

$$\sqrt{\frac{2.92114\times 10000000000000000000000000000000000000000000000000000000}{2.96}}$$

Multiply 2.92114 and 10000000000000000000000000000000000000000000000000000000 to get 29211400000000000000000000000000000000000000000000000000.

$$\sqrt{\frac{29211400000000000000000000000000000000000000000000000000}{2.96}}$$

Expand \frac{29211400000000000000000000000000000000000000000000000000}{2.96} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{2921140000000000000000000000000000000000000000000000000000}{296}}$$

Reduce the fraction \frac{2921140000000000000000000000000000000000000000000000000000}{296} to lowest terms by extracting and canceling out 8.

$$\sqrt{\frac{365142500000000000000000000000000000000000000000000000000}{37}}$$

Rewrite the square root of the division \sqrt{\frac{365142500000000000000000000000000000000000000000000000000}{37}} as the division of square roots \frac{\sqrt{365142500000000000000000000000000000000000000000000000000}}{\sqrt{37}}.

$$\frac{\sqrt{365142500000000000000000000000000000000000000000000000000}}{\sqrt{37}}$$

Factor 365142500000000000000000000000000000000000000000000000000=50000000000000000000000000^{2}\times 146057. Rewrite the square root of the product \sqrt{50000000000000000000000000^{2}\times 146057} as the product of square roots \sqrt{50000000000000000000000000^{2}}\sqrt{146057}. Take the square root of 50000000000000000000000000^{2}.

$$\frac{50000000000000000000000000\sqrt{146057}}{\sqrt{37}}$$

Rationalize the denominator of \frac{50000000000000000000000000\sqrt{146057}}{\sqrt{37}} by multiplying numerator and denominator by \sqrt{37}.

$$\frac{50000000000000000000000000\sqrt{146057}\sqrt{37}}{\left(\sqrt{37}\right)^{2}}$$

The square of \sqrt{37} is 37.

$$\frac{50000000000000000000000000\sqrt{146057}\sqrt{37}}{37}$$

To multiply \sqrt{146057} and \sqrt{37}, multiply the numbers under the square root.

$$\frac{50000000000000000000000000\sqrt{5404109}}{37}$$