Solve sqrt{3div4*10^2}

$$\sqrt{ 3 \div 4 \times { 10 }^{ 2 } }$$

Evaluate

$$5\sqrt{3}\approx 8.660254038$$

Solution Steps

Calculate 10 to the power of 2 and get 100.

$$\sqrt{\frac{3}{4}\times 100}$$

Express \frac{3}{4}\times 100 as a single fraction.

$$\sqrt{\frac{3\times 100}{4}}$$

Multiply 3 and 100 to get 300.

$$\sqrt{\frac{300}{4}}$$

Divide 300 by 4 to get 75.

$$\sqrt{75}$$

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$5\sqrt{3}$$