Solve (5sqrt{12})*(2sqrt{27})

$$(5 \sqrt{ 12 } ) \times (2 \sqrt{ 27 } )$$

Evaluate

$$180$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$5\times 2\sqrt{3}\times 2\sqrt{27}$$

Multiply 5 and 2 to get 10.

$$10\sqrt{3}\times 2\sqrt{27}$$

Multiply 10 and 2 to get 20.

$$20\sqrt{3}\sqrt{27}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

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

Multiply 20 and 3 to get 60.

$$60\sqrt{3}\sqrt{3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$60\times 3$$

Multiply 60 and 3 to get 180.

$$180$$

Factor

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