Question

$d = \sqrt{(5 - 3)^2 + (-3 + 1)}$
$\sqrt{(2)^2 + (-2)^2}$

Explanation:

Step1: Simplify the terms inside the square roots

First, calculate \((5 - 3)^2\) and \((-3 + 1)^2\) (assuming the second term was a typo and should be squared as it's part of the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)).
\((5 - 3)^2=(2)^2 = 4\)
\((-3 + 1)^2=(-2)^2 = 4\)

Step2: Add the simplified terms

Now add the two results from Step 1: \(4 + 4=8\)

Step3: Take the square root

Take the square root of the sum: \(d = \sqrt{8}\)
Simplify \(\sqrt{8}\) as \(2\sqrt{2}\) (since \(\sqrt{8}=\sqrt{4\times2}=\sqrt{4}\times\sqrt{2}=2\sqrt{2}\)) or as a decimal approximately \(2.828\). If we consider the calculation from the second square root in the image (where it's \(\sqrt{(2)^2+(-2)^2}\)), we have:
\(\sqrt{2^2+(-2)^2}=\sqrt{4 + 4}=\sqrt{8}=2\sqrt{2}\approx2.83\)

Answer:

If we simplify \(\sqrt{8}\), the exact value is \(2\sqrt{2}\) and the approximate decimal value is \(\approx2.83\) (depending on the required form). If we follow the second square root calculation \(\sqrt{(2)^2+(-2)^2}\), the result is \(2\sqrt{2}\) (or approximately \(2.83\)).