Solve -2sqrt{1100-8}-3(-1-2)+2sqrt{2}sqrt{8}-30divsqrt{5+4*5}

$$- 2 \sqrt { 1100 - 8 } - 3 ( - 1 - 2 ) + 2 \sqrt { 2 } \sqrt { 8 } - 30 \div \sqrt { 5 + 4 \times 5 }$$

Evaluate

$$11-4\sqrt{273}\approx -55.090846567$$

Solution Steps

Subtract 8 from 1100 to get 1092.

$$-2\sqrt{1092}-3\left(-1-2\right)+2\sqrt{2}\sqrt{8}-\frac{30}{\sqrt{5+4\times 5}}$$

Factor 1092=2^{2}\times 273. Rewrite the square root of the product \sqrt{2^{2}\times 273} as the product of square roots \sqrt{2^{2}}\sqrt{273}. Take the square root of 2^{2}.

$$-2\times 2\sqrt{273}-3\left(-1-2\right)+2\sqrt{2}\sqrt{8}-\frac{30}{\sqrt{5+4\times 5}}$$

Multiply -2 and 2 to get -4.

$$-4\sqrt{273}-3\left(-1-2\right)+2\sqrt{2}\sqrt{8}-\frac{30}{\sqrt{5+4\times 5}}$$

Subtract 2 from -1 to get -3.

$$-4\sqrt{273}-3\left(-3\right)+2\sqrt{2}\sqrt{8}-\frac{30}{\sqrt{5+4\times 5}}$$

Multiply 3 and -3 to get -9.

$$-4\sqrt{273}-\left(-9\right)+2\sqrt{2}\sqrt{8}-\frac{30}{\sqrt{5+4\times 5}}$$

The opposite of -9 is 9.

$$-4\sqrt{273}+9+2\sqrt{2}\sqrt{8}-\frac{30}{\sqrt{5+4\times 5}}$$

Factor 8=2\times 4. Rewrite the square root of the product \sqrt{2\times 4} as the product of square roots \sqrt{2}\sqrt{4}.

$$-4\sqrt{273}+9+2\sqrt{2}\sqrt{2}\sqrt{4}-\frac{30}{\sqrt{5+4\times 5}}$$

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

$$-4\sqrt{273}+9+2\times 2\sqrt{4}-\frac{30}{\sqrt{5+4\times 5}}$$

Multiply 2 and 2 to get 4.

$$-4\sqrt{273}+9+4\sqrt{4}-\frac{30}{\sqrt{5+4\times 5}}$$

Calculate the square root of 4 and get 2.

$$-4\sqrt{273}+9+4\times 2-\frac{30}{\sqrt{5+4\times 5}}$$

Multiply 4 and 2 to get 8.

$$-4\sqrt{273}+9+8-\frac{30}{\sqrt{5+4\times 5}}$$

Add 9 and 8 to get 17.

$$-4\sqrt{273}+17-\frac{30}{\sqrt{5+4\times 5}}$$

Multiply 4 and 5 to get 20.

$$-4\sqrt{273}+17-\frac{30}{\sqrt{5+20}}$$

Add 5 and 20 to get 25.

$$-4\sqrt{273}+17-\frac{30}{\sqrt{25}}$$

Calculate the square root of 25 and get 5.

$$-4\sqrt{273}+17-\frac{30}{5}$$

Divide 30 by 5 to get 6.

$$-4\sqrt{273}+17-6$$

Subtract 6 from 17 to get 11.

$$-4\sqrt{273}+11$$