Question

Which values make √x + 1 a whole number?

x = 5

x = 24

x = 15

x = -10

Answer 1

To determine which values make \( \sqrt{x} + 1 \) a whole number, we need \( \sqrt{x} \) to be a whole number itself. This means \( x \) must be a perfect square.

Let's check each value of \( x \):

1. **For \( x = 5 \)**:
\[
\sqrt{5} \approx 2.236 \quad \Rightarrow \quad \sqrt{5} + 1 \approx 3.236 \quad \text{(not a whole number)}
\]

2. **For \( x = 24 \)**:
\[
\sqrt{24} \approx 4.899 \quad \Rightarrow \quad \sqrt{24} + 1 \approx 5.899 \quad \text{(not a whole number)}
\]

3. **For \( x = 15 \)**:
\[
\sqrt{15} \approx 3.873 \quad \Rightarrow \quad \sqrt{15} + 1 \approx 4.873 \quad \text{(not a whole number)}
\]

4. **For \( x = -10 \)**:
\[
\sqrt{-10} \quad \text{(not defined in the set of real numbers)}
\]

None of the values of \( x = 5, 24, 15, \) or \( -10 \) make \( \sqrt{x} + 1 \) a whole number.

To make \( \sqrt{x} + 1 \) a whole number, \( x \) must be a perfect square (e.g., \( 0, 1, 4, 9, 16, 25, \) etc.).