Solve sqrt{24:8-[(2^4*2-2^2*3):(12:3+1)-8:2^3]+7*0+4*7:28}

$$\sqrt { 24 : 8 - [ ( 2 ^ { 4 } \cdot 2 - 2 ^ { 2 } \cdot 3 ) : ( 12 : 3 + 1 ) - 8 : 2 ^ { 3 } ] + 7 \cdot 0 + 4 \cdot 7 : 28 }$$

Evaluate

$$1$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$\sqrt{\frac{24}{8}-\left(\frac{2^{5}-2^{2}\times 3}{\frac{12}{3}+1}-\frac{8}{2^{3}}\right)+7\times 0+\frac{4\times 7}{28}}$$

Divide 24 by 8 to get 3.

$$\sqrt{3-\left(\frac{2^{5}-2^{2}\times 3}{\frac{12}{3}+1}-\frac{8}{2^{3}}\right)+7\times 0+\frac{4\times 7}{28}}$$

Calculate 2 to the power of 5 and get 32.

$$\sqrt{3-\left(\frac{32-2^{2}\times 3}{\frac{12}{3}+1}-\frac{8}{2^{3}}\right)+7\times 0+\frac{4\times 7}{28}}$$

Calculate 2 to the power of 2 and get 4.

$$\sqrt{3-\left(\frac{32-4\times 3}{\frac{12}{3}+1}-\frac{8}{2^{3}}\right)+7\times 0+\frac{4\times 7}{28}}$$

Multiply 4 and 3 to get 12.

$$\sqrt{3-\left(\frac{32-12}{\frac{12}{3}+1}-\frac{8}{2^{3}}\right)+7\times 0+\frac{4\times 7}{28}}$$

Subtract 12 from 32 to get 20.

$$\sqrt{3-\left(\frac{20}{\frac{12}{3}+1}-\frac{8}{2^{3}}\right)+7\times 0+\frac{4\times 7}{28}}$$

Divide 12 by 3 to get 4.

$$\sqrt{3-\left(\frac{20}{4+1}-\frac{8}{2^{3}}\right)+7\times 0+\frac{4\times 7}{28}}$$

Add 4 and 1 to get 5.

$$\sqrt{3-\left(\frac{20}{5}-\frac{8}{2^{3}}\right)+7\times 0+\frac{4\times 7}{28}}$$

Divide 20 by 5 to get 4.

$$\sqrt{3-\left(4-\frac{8}{2^{3}}\right)+7\times 0+\frac{4\times 7}{28}}$$

Calculate 2 to the power of 3 and get 8.

$$\sqrt{3-\left(4-\frac{8}{8}\right)+7\times 0+\frac{4\times 7}{28}}$$

Divide 8 by 8 to get 1.

$$\sqrt{3-\left(4-1\right)+7\times 0+\frac{4\times 7}{28}}$$

Subtract 1 from 4 to get 3.

$$\sqrt{3-3+7\times 0+\frac{4\times 7}{28}}$$

Subtract 3 from 3 to get 0.

$$\sqrt{0+7\times 0+\frac{4\times 7}{28}}$$

Multiply 7 and 0 to get 0.

$$\sqrt{0+0+\frac{4\times 7}{28}}$$

Add 0 and 0 to get 0.

$$\sqrt{\frac{4\times 7}{28}}$$

Multiply 4 and 7 to get 28.

$$\sqrt{\frac{28}{28}}$$

Divide 28 by 28 to get 1.

$$\sqrt{1}$$

Calculate the square root of 1 and get 1.

$$1$$

Factor

$$1$$