Solve 3sqrt{12}*-sqrt{76}

$$3 \sqrt { 12 } \cdot - \sqrt { 76 }$$

Evaluate

$$-12\sqrt{57}\approx -90.598013223$$

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}.

$$3\times 2\sqrt{3}\left(-\sqrt{76}\right)$$

Multiply 3 and 2 to get 6.

$$6\sqrt{3}\left(-\sqrt{76}\right)$$

Factor 76=2^{2}\times 19. Rewrite the square root of the product \sqrt{2^{2}\times 19} as the product of square roots \sqrt{2^{2}}\sqrt{19}. Take the square root of 2^{2}.

$$6\sqrt{3}\left(-2\sqrt{19}\right)$$

Multiply 6 and -1 to get -6.

$$-6\sqrt{3}\times 2\sqrt{19}$$

Multiply -6 and 2 to get -12.

$$-12\sqrt{3}\sqrt{19}$$

To multiply \sqrt{3} and \sqrt{19}, multiply the numbers under the square root.

$$-12\sqrt{57}$$