Solve sqrt{(35-2^{2}*2^3+6)*(7+20-3^3)+5^2}+sqrt{7^2+17*3}

$$\sqrt { ( 35 - 2 ^ { 2 } \cdot 2 ^ { 3 } + 6 ) \cdot ( 7 + 20 - 3 ^ { 3 } ) + 5 ^ { 2 } } + \sqrt { 7 ^ { 2 } + 17 \cdot 3 }$$

Evaluate

$$15$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\sqrt{\left(35-2^{5}+6\right)\left(7+20-3^{3}\right)+5^{2}}+\sqrt{7^{2}+17\times 3}$$

Calculate 2 to the power of 5 and get 32.

$$\sqrt{\left(35-32+6\right)\left(7+20-3^{3}\right)+5^{2}}+\sqrt{7^{2}+17\times 3}$$

Subtract 32 from 35 to get 3.

$$\sqrt{\left(3+6\right)\left(7+20-3^{3}\right)+5^{2}}+\sqrt{7^{2}+17\times 3}$$

Add 3 and 6 to get 9.

$$\sqrt{9\left(7+20-3^{3}\right)+5^{2}}+\sqrt{7^{2}+17\times 3}$$

Add 7 and 20 to get 27.

$$\sqrt{9\left(27-3^{3}\right)+5^{2}}+\sqrt{7^{2}+17\times 3}$$

Calculate 3 to the power of 3 and get 27.

$$\sqrt{9\left(27-27\right)+5^{2}}+\sqrt{7^{2}+17\times 3}$$

Subtract 27 from 27 to get 0.

$$\sqrt{9\times 0+5^{2}}+\sqrt{7^{2}+17\times 3}$$

Multiply 9 and 0 to get 0.

$$\sqrt{0+5^{2}}+\sqrt{7^{2}+17\times 3}$$

Calculate 5 to the power of 2 and get 25.

$$\sqrt{0+25}+\sqrt{7^{2}+17\times 3}$$

Add 0 and 25 to get 25.

$$\sqrt{25}+\sqrt{7^{2}+17\times 3}$$

Calculate the square root of 25 and get 5.

$$5+\sqrt{7^{2}+17\times 3}$$

Calculate 7 to the power of 2 and get 49.

$$5+\sqrt{49+17\times 3}$$

Multiply 17 and 3 to get 51.

$$5+\sqrt{49+51}$$

Add 49 and 51 to get 100.

$$5+\sqrt{100}$$

Calculate the square root of 100 and get 10.

$$5+10$$

Add 5 and 10 to get 15.

$$15$$

Factor

$$3\times 5$$