Question

$\sqrt{(3 - 2)^2 + (10 - 7)^2}$

Explanation:

Step1: Calculate inside the parentheses

First, we calculate the values inside each pair of parentheses. For the first part, \(3 - 2 = 1\), and for the second part, \(10 - 7 = 3\). So the expression becomes \(\sqrt{(1)^{2}+(3)^{2}}\).

Step2: Calculate the squares

Next, we calculate the squares of the results from Step 1. \(1^{2}=1\) and \(3^{2} = 9\). Now the expression is \(\sqrt{1 + 9}\).

Step3: Add the numbers inside the square root

Then we add the two numbers inside the square root: \(1+9 = 10\). So the expression simplifies to \(\sqrt{10}\). Wait, but there's a 17 at the bottom right, maybe I misread? Wait no, let's recalculate. Wait, \(3 - 2 = 1\), \(10 - 7 = 3\). Then \(1^2=1\), \(3^2 = 9\). Then \(1 + 9 = 10\), so \(\sqrt{10}\approx3.16\). But maybe the problem is to simplify or find the value? Wait, maybe I made a mistake. Wait, no, the formula is the distance formula between two points \((2,7)\) and \((3,10)\). So distance \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). So \(x_1 = 2\), \(x_2 = 3\), \(y_1 = 7\), \(y_2 = 10\). So \(d=\sqrt{(3 - 2)^2+(10 - 7)^2}=\sqrt{1 + 9}=\sqrt{10}\approx3.16\). But the 17 at the bottom right, maybe it's a typo or irrelevant? Wait, maybe the original problem was different? Wait, no, let's check again. Wait, \((3 - 2)=1\), \((10 - 7)=3\). Then \(1^2 + 3^2=1 + 9 = 10\), so square root of 10. But maybe the user wants the simplified radical or the decimal? Wait, the square root of 10 is approximately 3.16, but let's see. Wait, maybe I miscalculated. Wait, no, 1 squared is 1, 3 squared is 9, sum is 10, square root of 10. So the value is \(\sqrt{10}\) or approximately 3.16. But maybe the problem is to compute it. Let's do it step by step.

Step1: Compute differences

\(3 - 2 = 1\), \(10 - 7 = 3\)

Step2: Square the differences

\(1^2 = 1\), \(3^2 = 9\)

Step3: Sum the squares

\(1 + 9 = 10\)

Step4: Take the square root

\(\sqrt{10}\approx3.16\) (if decimal) or \(\sqrt{10}\) (exact form)

Wait, but the 17 at the bottom, maybe it's a mistake. But according to the expression given, the calculation is as above.

Answer:

\(\sqrt{10}\) (or approximately \(3.16\))