Solve 2*sqrt{5}*sqrt{10}*sqrt{162}

$$2 \times \sqrt { 5 } \times \sqrt { 10 } \times \sqrt { 162 }$$

Evaluate

$$180$$

Solution Steps

Factor 10=5\times 2. Rewrite the square root of the product \sqrt{5\times 2} as the product of square roots \sqrt{5}\sqrt{2}.

$$2\sqrt{5}\sqrt{5}\sqrt{2}\sqrt{162}$$

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

$$2\times 5\sqrt{2}\sqrt{162}$$

Factor 162=2\times 81. Rewrite the square root of the product \sqrt{2\times 81} as the product of square roots \sqrt{2}\sqrt{81}.

$$2\times 5\sqrt{2}\sqrt{2}\sqrt{81}$$

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

$$2\times 5\times 2\sqrt{81}$$

Multiply 2 and 5 to get 10.

$$10\times 2\sqrt{81}$$

Multiply 10 and 2 to get 20.

$$20\sqrt{81}$$

Calculate the square root of 81 and get 9.

$$20\times 9$$

Multiply 20 and 9 to get 180.

$$180$$

Factor

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