Solve sqrt{8-(18div3^2+3)+2*(13-10^3div10^2)}

$$\sqrt{ 8-(18 \div { 3 }^{ 2 } +3)+2 \times (13- { 10 }^{ 3 } \div { 10 }^{ 2 } ) }$$

Evaluate

$$3$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 3 to get 1.

$$\sqrt{8-\left(\frac{18}{3^{2}}+3\right)+2\left(13-10^{1}\right)}$$

Calculate 3 to the power of 2 and get 9.

$$\sqrt{8-\left(\frac{18}{9}+3\right)+2\left(13-10^{1}\right)}$$

Divide 18 by 9 to get 2.

$$\sqrt{8-\left(2+3\right)+2\left(13-10^{1}\right)}$$

Add 2 and 3 to get 5.

$$\sqrt{8-5+2\left(13-10^{1}\right)}$$

Subtract 5 from 8 to get 3.

$$\sqrt{3+2\left(13-10^{1}\right)}$$

Calculate 10 to the power of 1 and get 10.

$$\sqrt{3+2\left(13-10\right)}$$

Subtract 10 from 13 to get 3.

$$\sqrt{3+2\times 3}$$

Multiply 2 and 3 to get 6.

$$\sqrt{3+6}$$

Add 3 and 6 to get 9.

$$\sqrt{9}$$

Calculate the square root of 9 and get 3.

$$3$$

Factor

$$3$$