Solve sqrt{292114*10^36/296*10^-19}

$$\sqrt{ \frac{ 292114 \times { 10 }^{ 36 } }{ 296 \times { 10 }^{ -19 } } }$$

Evaluate

$$\frac{500000000000000000000000000\sqrt{54041090}}{37}\approx 9.934141239 \cdot 10^{28}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\sqrt{\frac{146057\times 10^{36}}{148\times 10^{-19}}}$$

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

$$\sqrt{\frac{146057\times 10^{55}}{148}}$$

Calculate 10 to the power of 55 and get 10000000000000000000000000000000000000000000000000000000.

$$\sqrt{\frac{146057\times 10000000000000000000000000000000000000000000000000000000}{148}}$$

Multiply 146057 and 10000000000000000000000000000000000000000000000000000000 to get 1460570000000000000000000000000000000000000000000000000000000.

$$\sqrt{\frac{1460570000000000000000000000000000000000000000000000000000000}{148}}$$

Reduce the fraction \frac{1460570000000000000000000000000000000000000000000000000000000}{148} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{365142500000000000000000000000000000000000000000000000000000}{37}}$$

Rewrite the square root of the division \sqrt{\frac{365142500000000000000000000000000000000000000000000000000000}{37}} as the division of square roots \frac{\sqrt{365142500000000000000000000000000000000000000000000000000000}}{\sqrt{37}}.

$$\frac{\sqrt{365142500000000000000000000000000000000000000000000000000000}}{\sqrt{37}}$$

Factor 365142500000000000000000000000000000000000000000000000000000=500000000000000000000000000^{2}\times 1460570. Rewrite the square root of the product \sqrt{500000000000000000000000000^{2}\times 1460570} as the product of square roots \sqrt{500000000000000000000000000^{2}}\sqrt{1460570}. Take the square root of 500000000000000000000000000^{2}.

$$\frac{500000000000000000000000000\sqrt{1460570}}{\sqrt{37}}$$

Rationalize the denominator of \frac{500000000000000000000000000\sqrt{1460570}}{\sqrt{37}} by multiplying numerator and denominator by \sqrt{37}.

$$\frac{500000000000000000000000000\sqrt{1460570}\sqrt{37}}{\left(\sqrt{37}\right)^{2}}$$

The square of \sqrt{37} is 37.

$$\frac{500000000000000000000000000\sqrt{1460570}\sqrt{37}}{37}$$

To multiply \sqrt{1460570} and \sqrt{37}, multiply the numbers under the square root.

$$\frac{500000000000000000000000000\sqrt{54041090}}{37}$$