Solve sqrt{[(2+2^{2}*3-24:6:2):2^{2}]^{2}+[2*(3^{2}-2^{2})-2^{3}]^{3}+(3^4:3^2-5)^3:2^3}

$$\sqrt { [ ( 2 + 2 ^ { 2 } \times 3 - 24 : 6 : 2 ) : 2 ^ { 2 } ] ^ { 2 } + [ 2 \times ( 3 ^ { 2 } - 2 ^ { 2 } ) - 2 ^ { 3 } ] ^ { 3 } + ( 3 ^ { 4 } : 3 ^ { 2 } - 5 ) ^ { 3 } : 2 ^ { 3 } }$$

Evaluate

$$5$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 4 to get 2.

$$\sqrt{\left(\frac{2+2^{2}\times 3-\frac{\frac{24}{6}}{2}}{2^{2}}\right)^{2}+\left(2\left(3^{2}-2^{2}\right)-2^{3}\right)^{3}+\frac{\left(3^{2}-5\right)^{3}}{2^{3}}}$$

Calculate 2 to the power of 2 and get 4.

$$\sqrt{\left(\frac{2+4\times 3-\frac{\frac{24}{6}}{2}}{2^{2}}\right)^{2}+\left(2\left(3^{2}-2^{2}\right)-2^{3}\right)^{3}+\frac{\left(3^{2}-5\right)^{3}}{2^{3}}}$$

Multiply 4 and 3 to get 12.

$$\sqrt{\left(\frac{2+12-\frac{\frac{24}{6}}{2}}{2^{2}}\right)^{2}+\left(2\left(3^{2}-2^{2}\right)-2^{3}\right)^{3}+\frac{\left(3^{2}-5\right)^{3}}{2^{3}}}$$

Add 2 and 12 to get 14.

$$\sqrt{\left(\frac{14-\frac{\frac{24}{6}}{2}}{2^{2}}\right)^{2}+\left(2\left(3^{2}-2^{2}\right)-2^{3}\right)^{3}+\frac{\left(3^{2}-5\right)^{3}}{2^{3}}}$$

Express \frac{\frac{24}{6}}{2} as a single fraction.

$$\sqrt{\left(\frac{14-\frac{24}{6\times 2}}{2^{2}}\right)^{2}+\left(2\left(3^{2}-2^{2}\right)-2^{3}\right)^{3}+\frac{\left(3^{2}-5\right)^{3}}{2^{3}}}$$

Multiply 6 and 2 to get 12.

$$\sqrt{\left(\frac{14-\frac{24}{12}}{2^{2}}\right)^{2}+\left(2\left(3^{2}-2^{2}\right)-2^{3}\right)^{3}+\frac{\left(3^{2}-5\right)^{3}}{2^{3}}}$$

Divide 24 by 12 to get 2.

$$\sqrt{\left(\frac{14-2}{2^{2}}\right)^{2}+\left(2\left(3^{2}-2^{2}\right)-2^{3}\right)^{3}+\frac{\left(3^{2}-5\right)^{3}}{2^{3}}}$$

Subtract 2 from 14 to get 12.

$$\sqrt{\left(\frac{12}{2^{2}}\right)^{2}+\left(2\left(3^{2}-2^{2}\right)-2^{3}\right)^{3}+\frac{\left(3^{2}-5\right)^{3}}{2^{3}}}$$

Calculate 2 to the power of 2 and get 4.

$$\sqrt{\left(\frac{12}{4}\right)^{2}+\left(2\left(3^{2}-2^{2}\right)-2^{3}\right)^{3}+\frac{\left(3^{2}-5\right)^{3}}{2^{3}}}$$

Divide 12 by 4 to get 3.

$$\sqrt{3^{2}+\left(2\left(3^{2}-2^{2}\right)-2^{3}\right)^{3}+\frac{\left(3^{2}-5\right)^{3}}{2^{3}}}$$

Calculate 3 to the power of 2 and get 9.

$$\sqrt{9+\left(2\left(3^{2}-2^{2}\right)-2^{3}\right)^{3}+\frac{\left(3^{2}-5\right)^{3}}{2^{3}}}$$

Calculate 3 to the power of 2 and get 9.

$$\sqrt{9+\left(2\left(9-2^{2}\right)-2^{3}\right)^{3}+\frac{\left(3^{2}-5\right)^{3}}{2^{3}}}$$

Calculate 2 to the power of 2 and get 4.

$$\sqrt{9+\left(2\left(9-4\right)-2^{3}\right)^{3}+\frac{\left(3^{2}-5\right)^{3}}{2^{3}}}$$

Subtract 4 from 9 to get 5.

$$\sqrt{9+\left(2\times 5-2^{3}\right)^{3}+\frac{\left(3^{2}-5\right)^{3}}{2^{3}}}$$

Multiply 2 and 5 to get 10.

$$\sqrt{9+\left(10-2^{3}\right)^{3}+\frac{\left(3^{2}-5\right)^{3}}{2^{3}}}$$

Calculate 2 to the power of 3 and get 8.

$$\sqrt{9+\left(10-8\right)^{3}+\frac{\left(3^{2}-5\right)^{3}}{2^{3}}}$$

Subtract 8 from 10 to get 2.

$$\sqrt{9+2^{3}+\frac{\left(3^{2}-5\right)^{3}}{2^{3}}}$$

Calculate 2 to the power of 3 and get 8.

$$\sqrt{9+8+\frac{\left(3^{2}-5\right)^{3}}{2^{3}}}$$

Add 9 and 8 to get 17.

$$\sqrt{17+\frac{\left(3^{2}-5\right)^{3}}{2^{3}}}$$

Calculate 3 to the power of 2 and get 9.

$$\sqrt{17+\frac{\left(9-5\right)^{3}}{2^{3}}}$$

Subtract 5 from 9 to get 4.

$$\sqrt{17+\frac{4^{3}}{2^{3}}}$$

Calculate 4 to the power of 3 and get 64.

$$\sqrt{17+\frac{64}{2^{3}}}$$

Calculate 2 to the power of 3 and get 8.

$$\sqrt{17+\frac{64}{8}}$$

Divide 64 by 8 to get 8.

$$\sqrt{17+8}$$

Add 17 and 8 to get 25.

$$\sqrt{25}$$

Calculate the square root of 25 and get 5.

$$5$$

Factor

$$5$$