Is 42 a square number?
Understand the Problem
The question is asking whether the number 42 can be expressed as the square of an integer. To determine this, we need to check if there exists an integer whose square equals 42.
Answer
No, $42$ cannot be expressed as the square of an integer.
Answer for screen readers
No, the number 42 cannot be expressed as the square of an integer.
Steps to Solve
- Determine the range of integers to check
We need to find integers $n$ such that $n^2 = 42$. To do this, we can take the square root of 42 to find our limits.
$$ n = \sqrt{42} \approx 6.48 $$
This means we should check integers from $0$ to $6$.
- Check each integer's square
Now, we will check the squares of the integers from $0$ to $6$:
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For $n = 0$: $$ 0^2 = 0 $$
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For $n = 1$: $$ 1^2 = 1 $$
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For $n = 2$: $$ 2^2 = 4 $$
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For $n = 3$: $$ 3^2 = 9 $$
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For $n = 4$: $$ 4^2 = 16 $$
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For $n = 5$: $$ 5^2 = 25 $$
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For $n = 6$: $$ 6^2 = 36 $$
- Conclusion about integer squares
After checking the squares of the integers $0$ to $6$, we find:
- None of these squares equal $42$.
Thus, there is no integer $n$ such that $n^2 = 42$.
No, the number 42 cannot be expressed as the square of an integer.
More Information
The number 42 is not a perfect square. Perfect squares are numbers like $0, 1, 4, 9, 16, 25, 36, 49$, etc. Each of these corresponds to the squares of integers.
Tips
- A common mistake is to confuse 42 with the nearest perfect squares (36 and 49) and assume it might be one of them.
- It's important to explicitly check all integer squares up to the calculated square root.
