Solve (3sqrt{8})(5sqrt{2}4)

$$( 3 \sqrt { 8 } ) ( 5 \sqrt { 2 } 4 )$$

Evaluate

$$240$$

Solution Steps

Factor 8=2\times 4. Rewrite the square root of the product \sqrt{2\times 4} as the product of square roots \sqrt{2}\sqrt{4}.

$$3\sqrt{2}\sqrt{4}\times 4\times 5\sqrt{2}$$

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

$$3\times 2\times 4\times 5\sqrt{4}$$

Multiply 3 and 2 to get 6.

$$6\times 4\times 5\sqrt{4}$$

Multiply 6 and 4 to get 24.

$$24\times 5\sqrt{4}$$

Multiply 24 and 5 to get 120.

$$120\sqrt{4}$$

Calculate the square root of 4 and get 2.

$$120\times 2$$

Multiply 120 and 2 to get 240.

$$240$$

Factor

$$2^{4}\times 3\times 5$$