Solve (3sqrt{50})(3sqrt{8})

$$( 3 \sqrt { 50 } ) ( 3 \sqrt { 8 } )$$

Evaluate

$$180$$

Solution Steps

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$3\times 5\sqrt{2}\times 3\sqrt{8}$$

Multiply 3 and 5 to get 15.

$$15\sqrt{2}\times 3\sqrt{8}$$

Multiply 15 and 3 to get 45.

$$45\sqrt{2}\sqrt{8}$$

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}.

$$45\sqrt{2}\times 2\sqrt{2}$$

Multiply 45 and 2 to get 90.

$$90\sqrt{2}\sqrt{2}$$

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

$$90\times 2$$

Multiply 90 and 2 to get 180.

$$180$$

Factor

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