Solve sqrt{15}sqrt{5}sqrt{27}

$$\sqrt{ 15 } \sqrt{ 5 } \sqrt{ 27 }$$

Evaluate

$$45$$

Solution Steps

Factor 15=5\times 3. Rewrite the square root of the product \sqrt{5\times 3} as the product of square roots \sqrt{5}\sqrt{3}.

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

Multiply \sqrt{5} and \sqrt{5} to get 5.

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

Factor 27=3\times 9. Rewrite the square root of the product \sqrt{3\times 9} as the product of square roots \sqrt{3}\sqrt{9}.

$$5\sqrt{3}\sqrt{3}\sqrt{9}$$

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

$$5\times 3\sqrt{9}$$

Multiply 5 and 3 to get 15.

$$15\sqrt{9}$$

Calculate the square root of 9 and get 3.

$$15\times 3$$

Multiply 15 and 3 to get 45.

$$45$$

Factor

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