Solve (3sqrt{12})(2sqrt{21})

$$( 3 \sqrt { 12 } ) ( 2 \sqrt { 21 } )$$

Evaluate

$$36\sqrt{7}\approx 95.247047198$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$3\times 2\sqrt{3}\times 2\sqrt{21}$$

Multiply 3 and 2 to get 6.

$$6\sqrt{3}\times 2\sqrt{21}$$

Multiply 6 and 2 to get 12.

$$12\sqrt{3}\sqrt{21}$$

Factor 21=3\times 7. Rewrite the square root of the product \sqrt{3\times 7} as the product of square roots \sqrt{3}\sqrt{7}.

$$12\sqrt{3}\sqrt{3}\sqrt{7}$$

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

$$12\times 3\sqrt{7}$$

Multiply 12 and 3 to get 36.

$$36\sqrt{7}$$