Solve sqrt{(-4)^2}=|-4|=4

$$\sqrt { ( - 4 ) ^ { 2 } } = | - 4 | = 4$$

Verify

Solution Steps

Calculate -4 to the power of 2 and get 16.

$$\sqrt{16}=|-4|\text{ and }|-4|=4$$

Calculate the square root of 16 and get 4.

$$4=|-4|\text{ and }|-4|=4$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -4 is 4.

$$4=4\text{ and }|-4|=4$$

Compare 4 and 4.

$$\text{true}\text{ and }|-4|=4$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -4 is 4.

$$\text{true}\text{ and }4=4$$

Compare 4 and 4.

$$\text{true}\text{ and }\text{true}$$

The conjunction of \text{true} and \text{true} is \text{true}.

$$\text{true}$$