Solve sqrt{45}*(-sqrt{48})

$$\sqrt { 45 } \times ( - \sqrt { 48 } )$$

Evaluate

$$-12\sqrt{15}\approx -46.475800154$$

Solution Steps

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

$$3\sqrt{5}\left(-\sqrt{48}\right)$$

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$3\sqrt{5}\left(-4\sqrt{3}\right)$$

Multiply 3 and -1 to get -3.

$$-3\sqrt{5}\times 4\sqrt{3}$$

Multiply -3 and 4 to get -12.

$$-12\sqrt{5}\sqrt{3}$$

To multiply \sqrt{5} and \sqrt{3}, multiply the numbers under the square root.

$$-12\sqrt{15}$$