Question

number line.
which expression could the point represent?
a. $\sqrt{26}$
b. $\sqrt{35}$
c. $\sqrt{37}$
d. $\sqrt{17}$

Explanation:

Step1: Identify point range

The point is between 5 and 6, so $5 < x < 6$.

Step2: Square all range terms

Square each part: $5^2 < x^2 < 6^2$, so $25 < x^2 < 36$.

Step3: Match to square roots

We need $\sqrt{n}$ where $25 < n < 36$.

• A. $\sqrt{26}$: $25<26<36$
• B. $\sqrt{35}$: $25<35<36$
• C. $\sqrt{37}$: $37>36$ (outside range)
• D. $\sqrt{17}$: $17<25$ (outside range)

Step4: Narrow to closer value

The point is near 5, so $x^2$ is closer to 25. $26$ is closer to 25 than $35$.

Answer:

A. $\sqrt{26}$