Solve frac{5sqrt{2}*sqrt{18}}{sqrt{36}}

$$\frac { 5 \sqrt { 2 } \cdot \sqrt { 18 } } { \sqrt { 36 } }$$

Evaluate

$$5$$

Solution Steps

Factor 18=2\times 9. Rewrite the square root of the product \sqrt{2\times 9} as the product of square roots \sqrt{2}\sqrt{9}.

$$\frac{5\sqrt{2}\sqrt{2}\sqrt{9}}{\sqrt{36}}$$

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

$$\frac{5\times 2\sqrt{9}}{\sqrt{36}}$$

Multiply 5 and 2 to get 10.

$$\frac{10\sqrt{9}}{\sqrt{36}}$$

Calculate the square root of 9 and get 3.

$$\frac{10\times 3}{\sqrt{36}}$$

Multiply 10 and 3 to get 30.

$$\frac{30}{\sqrt{36}}$$

Calculate the square root of 36 and get 6.

$$\frac{30}{6}$$

Divide 30 by 6 to get 5.

$$5$$

Factor

$$5$$