Solve sqrt{15:(6^2-7*5+2)+31}-sqrt{(2^3+6*7):10-6^0}

$$\sqrt { 15 : ( 6 ^ { 2 } - 7 \times 5 + 2 ) + 31 } - \sqrt { ( 2 ^ { 3 } + 6 \times 7 ) : 10 - 6 ^ { 0 } }$$

Evaluate

$$4$$

Solution Steps

Calculate 6 to the power of 2 and get 36.

$$\sqrt{\frac{15}{36-7\times 5+2}+31}-\sqrt{\frac{2^{3}+6\times 7}{10}-6^{0}}$$

Multiply 7 and 5 to get 35.

$$\sqrt{\frac{15}{36-35+2}+31}-\sqrt{\frac{2^{3}+6\times 7}{10}-6^{0}}$$

Subtract 35 from 36 to get 1.

$$\sqrt{\frac{15}{1+2}+31}-\sqrt{\frac{2^{3}+6\times 7}{10}-6^{0}}$$

Add 1 and 2 to get 3.

$$\sqrt{\frac{15}{3}+31}-\sqrt{\frac{2^{3}+6\times 7}{10}-6^{0}}$$

Divide 15 by 3 to get 5.

$$\sqrt{5+31}-\sqrt{\frac{2^{3}+6\times 7}{10}-6^{0}}$$

Add 5 and 31 to get 36.

$$\sqrt{36}-\sqrt{\frac{2^{3}+6\times 7}{10}-6^{0}}$$

Calculate the square root of 36 and get 6.

$$6-\sqrt{\frac{2^{3}+6\times 7}{10}-6^{0}}$$

Calculate 2 to the power of 3 and get 8.

$$6-\sqrt{\frac{8+6\times 7}{10}-6^{0}}$$

Multiply 6 and 7 to get 42.

$$6-\sqrt{\frac{8+42}{10}-6^{0}}$$

Add 8 and 42 to get 50.

$$6-\sqrt{\frac{50}{10}-6^{0}}$$

Divide 50 by 10 to get 5.

$$6-\sqrt{5-6^{0}}$$

Calculate 6 to the power of 0 and get 1.

$$6-\sqrt{5-1}$$

Subtract 1 from 5 to get 4.

$$6-\sqrt{4}$$

Calculate the square root of 4 and get 2.

$$6-2$$

Subtract 2 from 6 to get 4.

$$4$$

Factor

$$2^{2}$$