Solve 2sqrt{2}*5sqrt{3}*sqrt{6}

$$2 \sqrt { 2 } \cdot 5 \sqrt { 3 } \cdot \sqrt { 6 }$$

Evaluate

$$60$$

Solution Steps

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

$$2\times 5\sqrt{2}\sqrt{3}\sqrt{2}\sqrt{3}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$2\times 5\times 2\sqrt{3}\sqrt{3}$$

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

$$2\times 5\times 2\times 3$$

Multiply 2 and 5 to get 10.

$$10\times 2\times 3$$

Multiply 10 and 2 to get 20.

$$20\times 3$$

Multiply 20 and 3 to get 60.

$$60$$

Factor

$$2^{2}\times 3\times 5$$