Solve 3sqrt{18}*sqrt{50}

$$3 \sqrt { 18 } \cdot \sqrt { 50 }$$

Evaluate

$$90$$

Solution Steps

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$3\times 3\sqrt{2}\sqrt{50}$$

Multiply 3 and 3 to get 9.

$$9\sqrt{2}\sqrt{50}$$

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}.

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

Multiply 9 and 5 to get 45.

$$45\sqrt{2}\sqrt{2}$$

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

$$45\times 2$$

Multiply 45 and 2 to get 90.

$$90$$

Factor

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