Solve -6frac{sqrt{15}}{2}sqrt{45}

$$-6 \frac{ \sqrt{ 15 } }{ 2 } \sqrt{ 45 }$$

Evaluate

$$-45\sqrt{3}\approx -77.942286341$$

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}.

$$-6\times \frac{\sqrt{15}}{2}\times 3\sqrt{5}$$

Multiply -6 and 3 to get -18.

$$-18\times \frac{\sqrt{15}}{2}\sqrt{5}$$

Cancel out 2, the greatest common factor in 18 and 2.

$$-9\sqrt{15}\sqrt{5}$$

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}.

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

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

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

Multiply -9 and 5 to get -45.

$$-45\sqrt{3}$$