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# Square Numbers Trivia Quiz

### Square numbers are also known as perfect square numbers. This quiz tests your knowledge about these fascinating square numbers. Note that no commas are used in long numbers in 'Fill in the Blank' questions. Enjoy!

A multiple-choice quiz by Matthew_07. Estimated time: 6 mins.

Author
Time
6 mins
Type
Multiple Choice
Quiz #
292,892
Updated
Dec 03 21
# Qns
10
Difficulty
Average
Avg Score
7 / 10
Plays
3242
Awards
Top 20% Quiz
Last 3 plays: Dreessen (10/10), Guest 49 (8/10), Guest 152 (3/10).
Question 1 of 10
1. Square numbers can be expressed in the form of n^2, where n is any integer. Which of the following is NOT a square number? Hint

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Question 2 of 10
2. Choose the WRONG statement. Hint

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Question 3 of 10
3. Excluding 0 and 1, what is the smallest square number which is also a cube number?

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Question 4 of 10
4. The nth square numbers is also the sum of the first n ___ numbers.

Answer: (Odd or even?)

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Question 5 of 10
5. Given two integers m and n, you can find the difference of the squares of these two numbers by using the identity m^2 - n^2 = (m + n)(m - n). So what is the difference between the square of 51 and 49? In other words, what is 51^2 - 49^2?

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Question 6 of 10
6. A square number only ends in certain digits, so it is possible to determine whether a number given is a square number or not. Which of the following is NOT a square number? (Hint: try to find out first what digits can a square number end in) Hint

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Question 7 of 10
7. It may be tedious to find the square of a two-digit number because you have to perform a two-digit multiplication. However, for any two-digit number that ends in 5, there is a shorter and simpler way to compute its square. For example, you can calculate 25^2 = 625 easily by writing down the digits 25 first, then the digit precedes 25 is 2 x 3 = 6. The number 2 is from the first digit from the root 25, while the number 3 is obtained by adding 1 to 2, namely 2 + 1 = 3. Another example would be 45^2 = 2025, where the last two digits are 25. Then the digits precede 25 is 4 x 5 = 20. Now it's your turn. What is the square of 95?

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Question 8 of 10
8. Notice the following pattern:
1 x 1 = 1;
11 x 11 = 121;
111 x 111 = 12321
Now it's your turn. What is the square of 11111?

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Question 9 of 10
9. Given that the first few square numbers are 1, 4, 9, 16, 25 while the first few triangular numbers are 1, 3, 6, 10, 15. So what is the relationship between these two types of numbers? Hint

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Question 10 of 10
10. Is it possible for the sum of two different square numbers to be another square number?

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Most Recent Scores
Jul 15 2024 : Dreessen: 10/10
Jul 03 2024 : Guest 49: 8/10
Jun 05 2024 : Guest 152: 3/10
Jun 02 2024 : Guest 173: 9/10
May 30 2024 : Guest 223: 3/10

Score Distribution

Quiz Answer Key and Fun Facts
1. Square numbers can be expressed in the form of n^2, where n is any integer. Which of the following is NOT a square number?

The square root of 1 is 1. Meanwhile, 10 and 100 are the square roots of 100 and 10000 respectively. 10 is not a square number.

Notice that 1, 100, 10000, 1000000... are all square numbers but 10, 1000, 100000 are not.
2. Choose the WRONG statement.

Answer: There are some square numbers that are also prime numbers.

According to definition, a prime number is a number that is greater than 1 and has only the number 1 and the number itself as its proper divisor. So, 1 is not a prime number.

A square number cannot be a prime number because its root is one of the factors of the square number itself.

Notice that all square numbers are non-negative. We cannot say that all square numbers are positive because this would exclude the number 0, which is a square number.
3. Excluding 0 and 1, what is the smallest square number which is also a cube number?

Notice that 64 = 8^2 = 4^3.
4. The nth square numbers is also the sum of the first n ___ numbers.

For example, the 5th square number is 5^2 = 25, which can also be obtained by adding up the first 5 odd numbers, which is 1 + 3 + 5 + 7 + 9 = 25.
5. Given two integers m and n, you can find the difference of the squares of these two numbers by using the identity m^2 - n^2 = (m + n)(m - n). So what is the difference between the square of 51 and 49? In other words, what is 51^2 - 49^2?

51^2 - 49^2 = (51 + 49)(51 - 49) = 100 x 2 = 200
6. A square number only ends in certain digits, so it is possible to determine whether a number given is a square number or not. Which of the following is NOT a square number? (Hint: try to find out first what digits can a square number end in)

All square numbers end in either 0, 1, 4, 5, 6 or 9.

12345^2 = 152399025
19548^2 = 382124304
12223^2 = 149401729
7. It may be tedious to find the square of a two-digit number because you have to perform a two-digit multiplication. However, for any two-digit number that ends in 5, there is a shorter and simpler way to compute its square. For example, you can calculate 25^2 = 625 easily by writing down the digits 25 first, then the digit precedes 25 is 2 x 3 = 6. The number 2 is from the first digit from the root 25, while the number 3 is obtained by adding 1 to 2, namely 2 + 1 = 3. Another example would be 45^2 = 2025, where the last two digits are 25. Then the digits precede 25 is 4 x 5 = 20. Now it's your turn. What is the square of 95?

To find the square of 95, first write down the last two digits, namely 25. The digits precede 25 is 9 x 10 = 90. So the answer is 9025.
8. Notice the following pattern: 1 x 1 = 1; 11 x 11 = 121; 111 x 111 = 12321 Now it's your turn. What is the square of 11111?

This pattern will continue until 111111111 x 111111111 (nine 1's) = 12345678987654321.
9. Given that the first few square numbers are 1, 4, 9, 16, 25 while the first few triangular numbers are 1, 3, 6, 10, 15. So what is the relationship between these two types of numbers?

Answer: A square number is the sum of two consecutive triangular numbers.

For example, the sum of the second and third triangular numbers, 3 + 6 = 9 equals to the third square number.
10. Is it possible for the sum of two different square numbers to be another square number?

Yes, it is possible. This is the famous Pythagoras theorem, where a^2 + b^2 = c^2. Some Pythagoras triples are 3,4,5 and 5,12,13.
Source: Author Matthew_07

This quiz was reviewed by FunTrivia editor crisw before going online.
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Related Quizzes
This quiz is part of series Fun with Numbers:

A collection of my mathematics quizzes, covering different types of numbers with interesting properties. This list includes composite numbers, consecutive numbers, Fibonacci numbers, palindromic numbers, perfect numbers, prime numbers, square numbers, and triangular numbers.

1. Composite Numbers Average
2. Consecutive Numbers Average
3. Fibonacci Numbers Average
4. Palindromic Numbers Average
5. Perfect Numbers Average
6. Prime Numbers Tough
7. Square Numbers Average
8. Triangular Numbers Average

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