Question

Which values make square root X plus one a whole number
X = 5
X = 0
X = 15
X = -5

Answer 1

To determine which values make \(\sqrt{X} + 1\) a whole number, we can analyze each value of \(X\) given:

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

2. For \(X = 0\):
\[
\sqrt{0} + 1 = 0 + 1 = 1 \quad (\text{a whole number})
\]

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

4. For \(X = -5\):
The square root of a negative number is not a real number. Therefore:
\[
\sqrt{-5} + 1 \quad (\text{not a whole number, as it's undefined in the reals})
\]

From the values tested, the only one that makes \(\sqrt{X} + 1\) a whole number is:

- \(X = 0\) (resulting in 1).

So the answer is \(X = 0\).