Let's solve each problem step by step:
---
Problem 1: The perfect square number out of 2, 3, 4, and 5 is
- A perfect square is a number that can be expressed as the square of an integer.
- Check each option:
- \(2\) is not a perfect square.
- \(3\) is not a perfect square.
- \(4 = 2^2\), so \(4\) is a perfect square.
- \(5\) is not a perfect square.
- Therefore, the correct answer is:
\[
\boxed{c}
\]
---
Problem 2: Which of \(132^2\), \(87^2\), \(72^2\), and \(209^2\) would end with digit 1?
- To determine the last digit of a square, we only need to consider the last digit of the original number.
- Check the last digit of each number:
- \(132\) ends in \(2\). The square of \(2\) is \(4\), so \(132^2\) ends in \(4\).
- \(87\) ends in \(7\). The square of \(7\) is \(49\), so \(87^2\) ends in \(9\).
- \(72\) ends in \(2\). The square of \(2\) is \(4\), so \(72^2\) ends in \(4\).
- \(209\) ends in \(9\). The square of \(9\) is \(81\), so \(209^2\) ends in \(1\).
- Therefore, the correct answer is:
\[
\boxed{d}
\]
---
Problem 3: What will be the number of zeros in the square of the number 100?
- The number \(100\) can be written as \(10^2\).
- Squaring \(100\):
\[
100^2 = (10^2)^2 = 10^4 = 10000
\]
- The number \(10000\) has 4 zeros.
- Therefore, the correct answer is:
\[
\boxed{b}
\]
---
Problem 4: How many natural numbers lie between \(12^2\) and \(13^2\)?
- Calculate \(12^2\) and \(13^2\):
\[
12^2 = 144, \quad 13^2 = 169
\]
- The natural numbers between \(144\) and \(169\) are:
\[
145, 146, 147, \ldots, 168
\]
- To find the count, use the formula for the number of integers between two numbers \(a\) and \(b\) (inclusive):
\[
\text{Count} = b - a + 1
\]
Here, \(a = 145\) and \(b = 168\):
\[
\text{Count} = 168 - 145 + 1 = 24
\]
- Therefore, the correct answer is:
\[
\boxed{c}
\]
---
Problem 5: Express the square number \(5^2\) as the sum of two consecutive integers.
- Calculate \(5^2\):
\[
5^2 = 25
\]
- Let the two consecutive integers be \(n\) and \(n+1\). Their sum is:
\[
n + (n+1) = 2n + 1
\]
- Set this equal to \(25\):
\[
2n + 1 = 25
\]
- Solve for \(n\):
\[
2n = 24 \implies n = 12
\]
- The two consecutive integers are \(12\) and \(13\):
\[
12 + 13 = 25
\]
- Therefore, the correct answer is:
\[
\boxed{a}
\]
---
Final Answers:
1. \(\boxed{c}\)
2. \(\boxed{d}\)
3. \(\boxed{b}\)
4. \(\boxed{c}\)
5. \(\boxed{a}\)
Parent Tip: Review the logic above to help your child master the concept of square root worksheet 8th grade.
