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Main content

Squaring numbers

Introduction

In this article, you'll learn how to square numbers!

Example

Here's how we square the number 3:
3, squared, equals, 3, times, 3, equals, 9

Reflection question

What does it mean to square a number?
Choose 1 answer:
Choose 1 answer:

Practice

1, squared, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

2, squared, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

3, squared, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

4, times, 4, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

5, squared, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

6, squared, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

7, squared, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

8, times, 8, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

9, squared, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

10, squared, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

Challenge problem

a, squared, equals
Choose 1 answer:
Choose 1 answer:

Want to join the conversation?

  • starky tree style avatar for user derek.dragon.smith
    Why is it that when you do exponents of zero it is always 0
    (18 votes)
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  • blobby green style avatar for user stempluc000
    khan academy is a great site! ive learned a lot
    (11 votes)
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  • aqualine seed style avatar for user Leana Loranc
    In one of the tutorials the answer stated -1 to the 0 power is +1. I don't understand why. If you have a -1 and you times it by itself 0 times, wouldn't that leave you with -1?
    (8 votes)
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    • blobby green style avatar for user Nic Laatz
      So this is a trick of conventional logic vs mathematical rules. Don't confuse the absolute value of the event with whether or not the event happened. I'll explain.

      -1 times itself 0 times means that -1 was in fact multiplied by itself, the event happened, but to an exponent with an absolute value of 0. Therefore the absolute value of -1 is not affected, it remains 1, but the event still happened, so the signs also have to be multiplied, and a -x- is a +, hence the absolute value remains unchanged but the sign changes.

      I hope this makes sense, it is a difficult concept to explain.
      (4 votes)
  • blobby green style avatar for user 4541501128
    can you explian more plz
    (4 votes)
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  • starky seedling style avatar for user alicia
    what is an easy way to train your brain on multiplying the number that many times
    (1 vote)
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    • leaf green style avatar for user a.mueller3
      A lot of it is memorization, but there are also tricks. For example, 9 squared may not seem easy, but it is because 9 times 9 is not obvious, but 10 times 9 is and 9 times 9 is just one less. So you don't explicitly do 9 times 9, you do: (10x9)-9. Doesn't work for everything, but often there are tricks like that. Other example, 5 squared is half of 5x10, so it's just half of 50, and that's easier than actually multiplying 5 5 times in your head.


      Hope this helps.
      (6 votes)
  • piceratops seedling style avatar for user Connell, Mackenxo
    these exercises were not helpful at all they should give some separate spot for more experienced students.
    (3 votes)
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  • blobby green style avatar for user Janet Tsao Trump
    what is twice the value of 2 to the power of 15?
    (2 votes)
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  • mr pants purple style avatar for user Osemudiabhen
    how is the answer a*a how please any one answer me please
    (2 votes)
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  • blobby green style avatar for user 4541501128
    can you teach me faster
    (2 votes)
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  • piceratops seed style avatar for user 23mklema0910
    Khan Academy makes everything easier to learn especially math.
    (2 votes)
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