Solve 2sqrt{45}*sqrt{5/3}

$$2 \sqrt { 45 } \times \sqrt { \frac { 5 } { 3 } }$$

Evaluate

$$10\sqrt{3}\approx 17.320508076$$

Solution Steps

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

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

Multiply 2 and 3 to get 6.

$$6\sqrt{5}\sqrt{\frac{5}{3}}$$

Rewrite the square root of the division \sqrt{\frac{5}{3}} as the division of square roots \frac{\sqrt{5}}{\sqrt{3}}.

$$6\sqrt{5}\times \frac{\sqrt{5}}{\sqrt{3}}$$

Rationalize the denominator of \frac{\sqrt{5}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$6\sqrt{5}\times \frac{\sqrt{5}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$6\sqrt{5}\times \frac{\sqrt{5}\sqrt{3}}{3}$$

To multiply \sqrt{5} and \sqrt{3}, multiply the numbers under the square root.

$$6\sqrt{5}\times \frac{\sqrt{15}}{3}$$

Cancel out 3, the greatest common factor in 6 and 3.

$$2\sqrt{15}\sqrt{5}$$

Factor 15=5\times 3. Rewrite the square root of the product \sqrt{5\times 3} as the product of square roots \sqrt{5}\sqrt{3}.

$$2\sqrt{5}\sqrt{3}\sqrt{5}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

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

Multiply 2 and 5 to get 10.

$$10\sqrt{3}$$