Solve sqrt{3*10^5/2.7*10^3}

$$\sqrt{ \frac{ 3 \times { 10 }^{ 5 } }{ 2.7 \times { 10 }^{ 3 } } }$$

Evaluate

$$\frac{10\sqrt{10}}{3}\approx 10.540925534$$

Solution Steps

Cancel out 10^{3} in both numerator and denominator.

$$\sqrt{\frac{3\times 10^{2}}{2.7}}$$

Calculate 10 to the power of 2 and get 100.

$$\sqrt{\frac{3\times 100}{2.7}}$$

Multiply 3 and 100 to get 300.

$$\sqrt{\frac{300}{2.7}}$$

Expand \frac{300}{2.7} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{3000}{27}}$$

Reduce the fraction \frac{3000}{27} to lowest terms by extracting and canceling out 3.

$$\sqrt{\frac{1000}{9}}$$

Rewrite the square root of the division \sqrt{\frac{1000}{9}} as the division of square roots \frac{\sqrt{1000}}{\sqrt{9}}.

$$\frac{\sqrt{1000}}{\sqrt{9}}$$

Factor 1000=10^{2}\times 10. Rewrite the square root of the product \sqrt{10^{2}\times 10} as the product of square roots \sqrt{10^{2}}\sqrt{10}. Take the square root of 10^{2}.

$$\frac{10\sqrt{10}}{\sqrt{9}}$$

Calculate the square root of 9 and get 3.

$$\frac{10\sqrt{10}}{3}$$