Solve frac{sqrt{90}*sqrt{8}}{sqrt{20}}

$$\frac { \sqrt { 90 } \cdot \sqrt { 8 } } { \sqrt { 20 } }$$

Evaluate

$$6$$

Solution Steps

Factor 90=3^{2}\times 10. Rewrite the square root of the product \sqrt{3^{2}\times 10} as the product of square roots \sqrt{3^{2}}\sqrt{10}. Take the square root of 3^{2}.

$$\frac{3\sqrt{10}\sqrt{8}}{\sqrt{20}}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{3\sqrt{10}\times 2\sqrt{2}}{\sqrt{20}}$$

Multiply 3 and 2 to get 6.

$$\frac{6\sqrt{10}\sqrt{2}}{\sqrt{20}}$$

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

$$\frac{6\sqrt{2}\sqrt{5}\sqrt{2}}{\sqrt{20}}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{6\times 2\sqrt{5}}{\sqrt{20}}$$

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$\frac{6\times 2\sqrt{5}}{2\sqrt{5}}$$

Cancel out 2\sqrt{5} in both numerator and denominator.

$$2\times 3$$

Multiply 2 and 3 to get 6.

$$6$$

Factor

$$2\times 3$$