Question

error analysis: your math class is comparing $sqrt{11}$ and 5.1. your friend says that $sqrt{11}>5.1$ because $sqrt{11}=5.5$. what is the correct comparison? what mistake did your friend likely make?
what is the correct comparison?
$sqrt{11}$ $\boldsymbol{\blacktriangledown}$ 5.1

Explanation:

Step1: Calculate square of 5.1

To compare $\sqrt{11}$ and 5.1, first find $5.1^2$.
$5.1^2 = 5.1 \times 5.1 = 26.01$

Step2: Compare value to 11

Compare 11 with $5.1^2$.
$11 < 26.01$

Step3: Relate to square root inequality

Since $\sqrt{a} < b$ if $a < b^2$ for positive $a,b$, we get:
$\sqrt{11} < 5.1$

Step4: Identify friend's mistake

Friend confused $\sqrt{11}$ with $\sqrt{30.25}$, since $\sqrt{30.25}=5.5$. They likely mixed up 11 with 30.25, or confused $\sqrt{11}$ with $\sqrt{25}+0.5$.

Answer:

The correct comparison is $\boldsymbol{\sqrt{11} < 5.1}$.
Your friend likely confused $\sqrt{11}$ with $\sqrt{30.25}$ (which equals 5.1's incorrect claimed value of 5.5), or incorrectly calculated $\sqrt{11}$ by mixing it up with the square root of a larger number.