Question

rian draws a square section with side lengths of \\(\sqrt{2}\\) kilometers for camping. he thinks each side length of the camping area is 1.4 kilometers.\
se the drop - down menus to explain dorians reasoning.\
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dorian knows that the side length, \\(\sqrt{2}\\), squared is \\(\text{choose...}\\), but when he squares 1.4 on his calculator, he gets \\(\text{choose...}\\). the value of \\(\sqrt{2}\\) is \\(\text{choose...}\\) 1.4\
because the value of \\(\text{choose...}\\) squared is close to 2, dorians description of the side length is \\(\text{choose...}\\).

Explanation:

Step1: Square \(\sqrt{2}\)

Recall that \((\sqrt{a})^2 = a\) for \(a\geq0\). So, \((\sqrt{2})^2 = 2\).

Step2: Square \(1.4\)

Calculate \(1.4\times1.4\). \(1.4\times1.4 = 1.96\).

Step3: Compare \(\sqrt{2}\) and \(1.4\)

We know that if \(x^2\) is close to \(y^2\) and \(x,y>0\), then \(x\) is close to \(y\). Since \(1.4^2 = 1.96\) is close to \(2 = (\sqrt{2})^2\), and both \(\sqrt{2}\) and \(1.4\) are positive, \(\sqrt{2}\) is close to \(1.4\).

Step4: Evaluate Dorian's description

Because \(1.4^2 = 1.96\) is close to \(2\) (the square of \(\sqrt{2}\)), Dorian's description that the side length \(\sqrt{2}\) is approximately \(1.4\) is reasonable (or accurate in terms of approximation).

Answer:

• The side length \(\sqrt{2}\) squared is \(2\).
• When he squares \(1.4\), he gets \(1.96\).
• The value of \(\sqrt{2}\) is close to \(1.4\) because the value of \(1.4\) squared is close to \(2\).
• Dorian’s description of the side length is reasonable (or accurate as an approximation).