Solve sqrt{11+{17+[3*(29-2^3*2)+9*5]:(3*7)+(3^2-1):(4:2)}}

$$\sqrt { 11 + \{ 17 + [ 3 \cdot ( 29 - 2 ^ { 3 } \cdot 2 ) + 9 \cdot 5 ] : ( 3 \cdot 7 ) + ( 3 ^ { 2 } - 1 ) : ( 4 : 2 ) \} }$$

Evaluate

$$6$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\sqrt{11+17+\frac{3\left(29-2^{4}\right)+9\times 5}{3\times 7}+\frac{3^{2}-1}{\frac{4}{2}}}$$

Add 11 and 17 to get 28.

$$\sqrt{28+\frac{3\left(29-2^{4}\right)+9\times 5}{3\times 7}+\frac{3^{2}-1}{\frac{4}{2}}}$$

Calculate 2 to the power of 4 and get 16.

$$\sqrt{28+\frac{3\left(29-16\right)+9\times 5}{3\times 7}+\frac{3^{2}-1}{\frac{4}{2}}}$$

Subtract 16 from 29 to get 13.

$$\sqrt{28+\frac{3\times 13+9\times 5}{3\times 7}+\frac{3^{2}-1}{\frac{4}{2}}}$$

Multiply 3 and 13 to get 39.

$$\sqrt{28+\frac{39+9\times 5}{3\times 7}+\frac{3^{2}-1}{\frac{4}{2}}}$$

Multiply 9 and 5 to get 45.

$$\sqrt{28+\frac{39+45}{3\times 7}+\frac{3^{2}-1}{\frac{4}{2}}}$$

Add 39 and 45 to get 84.

$$\sqrt{28+\frac{84}{3\times 7}+\frac{3^{2}-1}{\frac{4}{2}}}$$

Multiply 3 and 7 to get 21.

$$\sqrt{28+\frac{84}{21}+\frac{3^{2}-1}{\frac{4}{2}}}$$

Divide 84 by 21 to get 4.

$$\sqrt{28+4+\frac{3^{2}-1}{\frac{4}{2}}}$$

Add 28 and 4 to get 32.

$$\sqrt{32+\frac{3^{2}-1}{\frac{4}{2}}}$$

Calculate 3 to the power of 2 and get 9.

$$\sqrt{32+\frac{9-1}{\frac{4}{2}}}$$

Subtract 1 from 9 to get 8.

$$\sqrt{32+\frac{8}{\frac{4}{2}}}$$

Divide 4 by 2 to get 2.

$$\sqrt{32+\frac{8}{2}}$$

Divide 8 by 2 to get 4.

$$\sqrt{32+4}$$

Add 32 and 4 to get 36.

$$\sqrt{36}$$

Calculate the square root of 36 and get 6.

$$6$$

Factor

$$2\times 3$$