Solve frac{sqrt{12}*sqrt{30}}{sqrt{90}}=?

$$\frac { \sqrt { 12 } \cdot \sqrt { 30 } } { \sqrt { 90 } } = ?$$

Evaluate

$$2$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\frac{2\sqrt{3}\sqrt{30}}{\sqrt{90}}$$

Factor 30=3\times 10. Rewrite the square root of the product \sqrt{3\times 10} as the product of square roots \sqrt{3}\sqrt{10}.

$$\frac{2\sqrt{3}\sqrt{3}\sqrt{10}}{\sqrt{90}}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{2\times 3\sqrt{10}}{\sqrt{90}}$$

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}.

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

Cancel out 3\sqrt{10} in both numerator and denominator.

$$2$$

Factor

$$2$$