Solve frac{sqrt{1.8*10^6}}{sqrt{0.2*10^4}}

$$\frac { \sqrt { 1.8 \times 10 ^ { 6 } } } { \sqrt { 0.2 \times 10 ^ { 4 } } }$$

Evaluate

$$30$$

Solution Steps

Calculate 10 to the power of 6 and get 1000000.

$$\frac{\sqrt{1.8\times 1000000}}{\sqrt{0.2\times 10^{4}}}$$

Multiply 1.8 and 1000000 to get 1800000.

$$\frac{\sqrt{1800000}}{\sqrt{0.2\times 10^{4}}}$$

Factor 1800000=600^{2}\times 5. Rewrite the square root of the product \sqrt{600^{2}\times 5} as the product of square roots \sqrt{600^{2}}\sqrt{5}. Take the square root of 600^{2}.

$$\frac{600\sqrt{5}}{\sqrt{0.2\times 10^{4}}}$$

Calculate 10 to the power of 4 and get 10000.

$$\frac{600\sqrt{5}}{\sqrt{0.2\times 10000}}$$

Multiply 0.2 and 10000 to get 2000.

$$\frac{600\sqrt{5}}{\sqrt{2000}}$$

Factor 2000=20^{2}\times 5. Rewrite the square root of the product \sqrt{20^{2}\times 5} as the product of square roots \sqrt{20^{2}}\sqrt{5}. Take the square root of 20^{2}.

$$\frac{600\sqrt{5}}{20\sqrt{5}}$$

Cancel out 20\sqrt{5} in both numerator and denominator.

$$30$$

Factor

$$2\times 3\times 5$$