Solve 2sqrt{15}*sqrt{5}-sqrt{96}:sqrt{2}

$$2 \sqrt { 15 } \times \sqrt { 5 } - \sqrt { 96 } : \sqrt { 2 }$$

Evaluate

$$6\sqrt{3}\approx 10.392304845$$

Solution Steps

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}.

$$2\sqrt{5}\sqrt{3}\sqrt{5}-\frac{\sqrt{96}}{\sqrt{2}}$$

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

$$2\times 5\sqrt{3}-\frac{\sqrt{96}}{\sqrt{2}}$$

Multiply 2 and 5 to get 10.

$$10\sqrt{3}-\frac{\sqrt{96}}{\sqrt{2}}$$

Rewrite the division of square roots \frac{\sqrt{96}}{\sqrt{2}} as the square root of the division \sqrt{\frac{96}{2}} and perform the division.

$$10\sqrt{3}-\sqrt{48}$$

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}.

$$10\sqrt{3}-4\sqrt{3}$$

Combine 10\sqrt{3} and -4\sqrt{3} to get 6\sqrt{3}.

$$6\sqrt{3}$$