Solve (sqrt{12})(sqrt{3})(sqrt{125})

$$( \sqrt { 12 } ) ( \sqrt { 3 } ) ( \sqrt { 125 } )$$

Evaluate

$$30\sqrt{5}\approx 67.082039325$$

Solution Steps

Factor 12=3\times 4. Rewrite the square root of the product \sqrt{3\times 4} as the product of square roots \sqrt{3}\sqrt{4}.

$$\sqrt{3}\sqrt{4}\sqrt{3}\sqrt{125}$$

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

$$3\sqrt{4}\sqrt{125}$$

Calculate the square root of 4 and get 2.

$$3\times 2\sqrt{125}$$

Multiply 3 and 2 to get 6.

$$6\sqrt{125}$$

Factor 125=5^{2}\times 5. Rewrite the square root of the product \sqrt{5^{2}\times 5} as the product of square roots \sqrt{5^{2}}\sqrt{5}. Take the square root of 5^{2}.

$$6\times 5\sqrt{5}$$

Multiply 6 and 5 to get 30.

$$30\sqrt{5}$$