Solve sqrt{75}*sqrt{27}=

$$\sqrt { 75 } \cdot \sqrt { 27 } =$$

Evaluate

$$45$$

Solution Steps

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$5\sqrt{3}\sqrt{27}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

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

Multiply 5 and 3 to get 15.

$$15\sqrt{3}\sqrt{3}$$

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

$$15\times 3$$

Multiply 15 and 3 to get 45.

$$45$$

Factor

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