Solve 3sqrt{200div7.6}

$$3 \sqrt{ 200 \div 7.6 }$$

Evaluate

$$\frac{30\sqrt{95}}{19}\approx 15.389675281$$

Solution Steps

Expand \frac{200}{7.6} by multiplying both numerator and the denominator by 10.

$$3\sqrt{\frac{2000}{76}}$$

Reduce the fraction \frac{2000}{76} to lowest terms by extracting and canceling out 4.

$$3\sqrt{\frac{500}{19}}$$

Rewrite the square root of the division \sqrt{\frac{500}{19}} as the division of square roots \frac{\sqrt{500}}{\sqrt{19}}.

$$3\times \frac{\sqrt{500}}{\sqrt{19}}$$

Factor 500=10^{2}\times 5. Rewrite the square root of the product \sqrt{10^{2}\times 5} as the product of square roots \sqrt{10^{2}}\sqrt{5}. Take the square root of 10^{2}.

$$3\times \frac{10\sqrt{5}}{\sqrt{19}}$$

Rationalize the denominator of \frac{10\sqrt{5}}{\sqrt{19}} by multiplying numerator and denominator by \sqrt{19}.

$$3\times \frac{10\sqrt{5}\sqrt{19}}{\left(\sqrt{19}\right)^{2}}$$

The square of \sqrt{19} is 19.

$$3\times \frac{10\sqrt{5}\sqrt{19}}{19}$$

To multiply \sqrt{5} and \sqrt{19}, multiply the numbers under the square root.

$$3\times \frac{10\sqrt{95}}{19}$$

Express 3\times \frac{10\sqrt{95}}{19} as a single fraction.

$$\frac{3\times 10\sqrt{95}}{19}$$

Multiply 3 and 10 to get 30.

$$\frac{30\sqrt{95}}{19}$$