Solve (2sqrt{45})(2sqrt{80})(sqrt{25})

$$( 2 \sqrt { 45 } ) ( 2 \sqrt { 80 } ) ( \sqrt { 25 } )$$

Evaluate

$$1200$$

Solution Steps

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

$$2\times 3\sqrt{5}\times 2\sqrt{80}\sqrt{25}$$

Multiply 2 and 3 to get 6.

$$6\sqrt{5}\times 2\sqrt{80}\sqrt{25}$$

Multiply 6 and 2 to get 12.

$$12\sqrt{5}\sqrt{80}\sqrt{25}$$

Factor 80=4^{2}\times 5. Rewrite the square root of the product \sqrt{4^{2}\times 5} as the product of square roots \sqrt{4^{2}}\sqrt{5}. Take the square root of 4^{2}.

$$12\sqrt{5}\times 4\sqrt{5}\sqrt{25}$$

Multiply 12 and 4 to get 48.

$$48\sqrt{5}\sqrt{5}\sqrt{25}$$

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

$$48\times 5\sqrt{25}$$

Calculate the square root of 25 and get 5.

$$48\times 5\times 5$$

Multiply 48 and 5 to get 240.

$$240\times 5$$

Multiply 240 and 5 to get 1200.

$$1200$$

Factor

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