Solve sqrt[2]{1+3|-(4)^2-(-8)|+2(3+(-5)^2)}

$$\sqrt[ 2 ] { 1 + 3 | - ( 4 ) ^ { 2 } - ( - 8 ) | + 2 ( 3 + ( - 5 ) ^ { 2 } ) }$$

Evaluate

$$9$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

$$\sqrt[2]{1+3|-16-\left(-8\right)|+2\left(3+\left(-5\right)^{2}\right)}$$

The opposite of -8 is 8.

$$\sqrt[2]{1+3|-16+8|+2\left(3+\left(-5\right)^{2}\right)}$$

Add -16 and 8 to get -8.

$$\sqrt[2]{1+3|-8|+2\left(3+\left(-5\right)^{2}\right)}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -8 is 8.

$$\sqrt[2]{1+3\times 8+2\left(3+\left(-5\right)^{2}\right)}$$

Multiply 3 and 8 to get 24.

$$\sqrt[2]{1+24+2\left(3+\left(-5\right)^{2}\right)}$$

Add 1 and 24 to get 25.

$$\sqrt[2]{25+2\left(3+\left(-5\right)^{2}\right)}$$

Calculate -5 to the power of 2 and get 25.

$$\sqrt[2]{25+2\left(3+25\right)}$$

Add 3 and 25 to get 28.

$$\sqrt[2]{25+2\times 28}$$

Multiply 2 and 28 to get 56.

$$\sqrt[2]{25+56}$$

Add 25 and 56 to get 81.

$$\sqrt[2]{81}$$

Calculate \sqrt[2]{81} and get 9.

$$9$$

Factor

$$3^{2}$$