Solve sqrt(\{(- 2) - 2\} ^ 2 + \{2 - (- 2)\} ^ 2) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\sqrt{\{(-2)-2\}^{2}+\{2-(-2)\}^{2}}$$

Evaluate

$4\sqrt{2}\approx 5.656854249$

Solution Steps

Subtract $2$ from $-2$ to get $-4$.

$$\sqrt{\left(-4\right)^{2}+\left(2-\left(-2\right)\right)^{2}}$$

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

$$\sqrt{16+\left(2-\left(-2\right)\right)^{2}}$$

The opposite of $-2$ is $2$.

$$\sqrt{16+\left(2+2\right)^{2}}$$

Add $2$ and $2$ to get $4$.

$$\sqrt{16+4^{2}}$$

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

$$\sqrt{16+16}$$

Add $16$ and $16$ to get $32$.

$$\sqrt{32}$$

Factor $32=4^{2}\times 2$. Rewrite the square root of the product $\sqrt{4^{2}\times 2}$ as the product of square roots $\sqrt{4^{2}}\sqrt{2}$. Take the square root of $4^{2}$.

$$4\sqrt{2}$$