Solve sqrt{910^-6}sqrt{0.0049}sqrt{2.510^3}

$$\sqrt{ 9 { 10 }^{ -6 } } \sqrt{ 0.0049 } \sqrt{ 2.5 { 10 }^{ 3 } }$$

Evaluate

$$0.0105$$

Solution Steps

Calculate 10 to the power of -6 and get \frac{1}{1000000}.

$$\sqrt{9\times \frac{1}{1000000}}\sqrt{0.0049}\sqrt{2.5\times 10^{3}}$$

Multiply 9 and \frac{1}{1000000} to get \frac{9}{1000000}.

$$\sqrt{\frac{9}{1000000}}\sqrt{0.0049}\sqrt{2.5\times 10^{3}}$$

Rewrite the square root of the division \frac{9}{1000000} as the division of square roots \frac{\sqrt{9}}{\sqrt{1000000}}. Take the square root of both numerator and denominator.

$$\frac{3}{1000}\sqrt{0.0049}\sqrt{2.5\times 10^{3}}$$

Calculate the square root of 0.0049 and get 0.07.

$$\frac{3}{1000}\times 0.07\sqrt{2.5\times 10^{3}}$$

Multiply \frac{3}{1000} and 0.07 to get \frac{21}{100000}.

$$\frac{21}{100000}\sqrt{2.5\times 10^{3}}$$

Calculate 10 to the power of 3 and get 1000.

$$\frac{21}{100000}\sqrt{2.5\times 1000}$$

Multiply 2.5 and 1000 to get 2500.

$$\frac{21}{100000}\sqrt{2500}$$

Calculate the square root of 2500 and get 50.

$$\frac{21}{100000}\times 50$$

Multiply \frac{21}{100000} and 50 to get \frac{21}{2000}.

$$\frac{21}{2000}$$

Factor

$$\frac{3 \cdot 7}{2 ^ {4} \cdot 5 ^ {3}} = 0.0105$$