Solve (5sqrt{8})(2sqrt{6}

$$( 5 \sqrt { 8 } ) ( 2 \sqrt { 6 }$$

Evaluate

$$40\sqrt{3}\approx 69.282032303$$

Solution Steps

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

$$5\times 2\sqrt{2}\times 2\sqrt{6}$$

Multiply 5 and 2 to get 10.

$$10\sqrt{2}\times 2\sqrt{6}$$

Multiply 10 and 2 to get 20.

$$20\sqrt{2}\sqrt{6}$$

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}.

$$20\sqrt{2}\sqrt{2}\sqrt{3}$$

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

$$20\times 2\sqrt{3}$$

Multiply 20 and 2 to get 40.

$$40\sqrt{3}$$