How can I square a large number?

What are square numbers?

If you multiply a number by itself, you get one Square number. The arithmetic operation is called Squaring.

Examples

  • 2$$*$$2 = 2² = 4
  • 3$$*$$3 = 3² = 9
  • 5$$*$$5 = 5² = 25
  • 10$$*$$10 = 10² = 100
  • 15$$*$$15 = 15² = 225
  • 20$$*$$20 = 20² = 400
  • 1$$*$$1 = 1² =1

The Squaring is a multiplication with two equal factors.

  • If you add 3 + 3 or 5 + 5, you can do the math 2 · 3 or 2 · 5.
  • addition with two equal summands is one multiplication with a factor of 2.
  • Notation: 3 + 3 = 2 3 = 6 and 5 + 5 = 2 · 5 = 10

Squares and square numbers

You actually know the word “square” from geometry. This square where all sides are the same length and where all angles are 90 °. What does this have to do with these numbers?

Determine the side lengths of the squares and the number of small squares inside:


This is how it looks, there you have the square numbers again:

Side length small squares
2 4
3 9
4 16

Squares of the multiplication table

For many tasks it is good if you know the square numbers from 1 to 10 by heart.

  • 1² = 1
  • 2² = 4
  • 3² = 9
  • 4² = 16
  • 5² = 25
  • 6² = 36
  • 7² = 49
  • 8² = 64
  • 9² = 81
  • 10² = 100

Small donkey bridges:
"Six times six is ​​thirty-six, all children do maths".
"Eight times eight is sixty-four, what you don't learn will take revenge."

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Big square numbers

In all honesty, it will also help you if you know the square numbers up to 20.

  • 11² = 121
  • 12² = 144
  • 13² = 169
  • 14² = 196
  • 15² = 225
  • 16² = 256
  • 17² = 289
  • 18² = 324
  • 19² = 361
  • 20² = 400

But of course you can always calculate 11 $$ * $$ 11 or 12 $$ * $$ 12 in your head as normal. Just takes longer.

You can also use the "arithmetic tricks" for large square numbers. Example:
34² = (30 + 4)² = 900 + 16 + 2 · 30 · 4
34² = 900 + 16 + 240 = 1156

From the square to a power of two

Not only can you multiply a number once, but you can also multiply several times.

This is important for the 2, but not so for other numbers.

$$2*2= 2^2 = 4$$
$$2 · 2 · 2 = 2 ^3 = 8$$
$$2 · 2 · 2 · 2 = 2 ^4 = 16$$
$$2 · 2 · 2 · 2 · 2 = 2 ^5 = 32$$
$$2 · 2 · 2 · 2 · 2 *2 = 2 ^6 = 64$$

All of these products with the number 2 are called Potencies from 2.

You can write a product of equal numbers as a power.
Example: $$2 * 2 * 2 * 2 * 2 = 2^5$$
say: 2 high 5