Solve 3sqrt{50/7}

$$3 \sqrt{ \frac{ 50 }{ 7 } }$$

Evaluate

$$\frac{15\sqrt{14}}{7}\approx 8.017837257$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{50}{7}} as the division of square roots \frac{\sqrt{50}}{\sqrt{7}}.

$$3\times \frac{\sqrt{50}}{\sqrt{7}}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$3\times \frac{5\sqrt{2}}{\sqrt{7}}$$

Rationalize the denominator of \frac{5\sqrt{2}}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$3\times \frac{5\sqrt{2}\sqrt{7}}{\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$3\times \frac{5\sqrt{2}\sqrt{7}}{7}$$

To multiply \sqrt{2} and \sqrt{7}, multiply the numbers under the square root.

$$3\times \frac{5\sqrt{14}}{7}$$

Express 3\times \frac{5\sqrt{14}}{7} as a single fraction.

$$\frac{3\times 5\sqrt{14}}{7}$$

Multiply 3 and 5 to get 15.

$$\frac{15\sqrt{14}}{7}$$