Solve sqrt{2*6.7*10^9/9.1*10^-3}

$$\sqrt{ \frac{ 2 \times 6.7 \times { 10 }^{ 9 } }{ 9.1 \times { 10 }^{ -3 } } }$$

Evaluate

$$\frac{1000000\sqrt{12194}}{91}\approx 1213477.429756101$$

Solution Steps

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

$$\sqrt{\frac{2\times 6.7\times 10^{12}}{9.1}}$$

Multiply 2 and 6.7 to get 13.4.

$$\sqrt{\frac{13.4\times 10^{12}}{9.1}}$$

Calculate 10 to the power of 12 and get 1000000000000.

$$\sqrt{\frac{13.4\times 1000000000000}{9.1}}$$

Multiply 13.4 and 1000000000000 to get 13400000000000.

$$\sqrt{\frac{13400000000000}{9.1}}$$

Expand \frac{13400000000000}{9.1} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{134000000000000}{91}}$$

Rewrite the square root of the division \sqrt{\frac{134000000000000}{91}} as the division of square roots \frac{\sqrt{134000000000000}}{\sqrt{91}}.

$$\frac{\sqrt{134000000000000}}{\sqrt{91}}$$

Factor 134000000000000=1000000^{2}\times 134. Rewrite the square root of the product \sqrt{1000000^{2}\times 134} as the product of square roots \sqrt{1000000^{2}}\sqrt{134}. Take the square root of 1000000^{2}.

$$\frac{1000000\sqrt{134}}{\sqrt{91}}$$

Rationalize the denominator of \frac{1000000\sqrt{134}}{\sqrt{91}} by multiplying numerator and denominator by \sqrt{91}.

$$\frac{1000000\sqrt{134}\sqrt{91}}{\left(\sqrt{91}\right)^{2}}$$

The square of \sqrt{91} is 91.

$$\frac{1000000\sqrt{134}\sqrt{91}}{91}$$

To multiply \sqrt{134} and \sqrt{91}, multiply the numbers under the square root.

$$\frac{1000000\sqrt{12194}}{91}$$