Solve 3sqrt{27}+4sqrt{9}-4sqrt{27}+4sqrt{243}-4sqrt{9}

$$3 \sqrt{ 27 } +4 \sqrt{ 9 } -4 \sqrt{ 27 } +4 \sqrt{ 243 } -4 \sqrt{ 9 }$$

Evaluate

$$33\sqrt{3}\approx 57.15767665$$

Solution Steps

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}.

$$3\times 3\sqrt{3}+4\sqrt{9}-4\sqrt{27}+4\sqrt{243}-4\sqrt{9}$$

Multiply 3 and 3 to get 9.

$$9\sqrt{3}+4\sqrt{9}-4\sqrt{27}+4\sqrt{243}-4\sqrt{9}$$

Calculate the square root of 9 and get 3.

$$9\sqrt{3}+4\times 3-4\sqrt{27}+4\sqrt{243}-4\sqrt{9}$$

Multiply 4 and 3 to get 12.

$$9\sqrt{3}+12-4\sqrt{27}+4\sqrt{243}-4\sqrt{9}$$

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}.

$$9\sqrt{3}+12-4\times 3\sqrt{3}+4\sqrt{243}-4\sqrt{9}$$

Multiply -4 and 3 to get -12.

$$9\sqrt{3}+12-12\sqrt{3}+4\sqrt{243}-4\sqrt{9}$$

Combine 9\sqrt{3} and -12\sqrt{3} to get -3\sqrt{3}.

$$-3\sqrt{3}+12+4\sqrt{243}-4\sqrt{9}$$

Factor 243=9^{2}\times 3. Rewrite the square root of the product \sqrt{9^{2}\times 3} as the product of square roots \sqrt{9^{2}}\sqrt{3}. Take the square root of 9^{2}.

$$-3\sqrt{3}+12+4\times 9\sqrt{3}-4\sqrt{9}$$

Multiply 4 and 9 to get 36.

$$-3\sqrt{3}+12+36\sqrt{3}-4\sqrt{9}$$

Combine -3\sqrt{3} and 36\sqrt{3} to get 33\sqrt{3}.

$$33\sqrt{3}+12-4\sqrt{9}$$

Calculate the square root of 9 and get 3.

$$33\sqrt{3}+12-4\times 3$$

Multiply -4 and 3 to get -12.

$$33\sqrt{3}+12-12$$

Subtract 12 from 12 to get 0.

$$33\sqrt{3}$$