# 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."

*kapiert.de*can do more:

- interactive exercises

and tests - individual classwork trainer
- Learning manager

### 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**

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