Solve 2sqrt{3}(3sqrt{75}-sqrt{12}-sqrt{27})

$$2 \sqrt{ 3 } (3 \sqrt{ 75 } - \sqrt{ 12 } - \sqrt{ 27 } )$$

Evaluate

$$60$$

Solution Steps

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$2\sqrt{3}\left(3\times 5\sqrt{3}-\sqrt{12}-\sqrt{27}\right)$$

Multiply 3 and 5 to get 15.

$$2\sqrt{3}\left(15\sqrt{3}-\sqrt{12}-\sqrt{27}\right)$$

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}.

$$2\sqrt{3}\left(15\sqrt{3}-2\sqrt{3}-\sqrt{27}\right)$$

Combine 15\sqrt{3} and -2\sqrt{3} to get 13\sqrt{3}.

$$2\sqrt{3}\left(13\sqrt{3}-\sqrt{27}\right)$$

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}.

$$2\sqrt{3}\left(13\sqrt{3}-3\sqrt{3}\right)$$

Combine 13\sqrt{3} and -3\sqrt{3} to get 10\sqrt{3}.

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

Multiply 2 and 10 to get 20.

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

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

$$20\times 3$$

Multiply 20 and 3 to get 60.

$$60$$

Factor

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