Square Numbers

​When we multiply a number by itself, we square the number.

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For example: The square of 4 is 4 × 4 = 16

​We write it as 4 × 4 = 4²

so, 4 × 4 = 4² = 16

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​We say: Four squared is sixteen.

16 is a square number, or a perfect square.​

Square numbers​

One way to model a square number is to draw a square

whose area is equal to the square number.​

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Show that 49 is a square number.

Use a diagram, symbols, and words.

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​Draw a square with area 49 square units.

The side length of the square is 7 units.

Then, 49 = 7 × 7 = 72²

We say: Forty-nine is seven squared.

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Square Numbers

​1	​2	​3	​4	​5	​6	​7
​8	​9	​10	​11	​12	​13	​14
​15	​16	​17	​18	​19	​20	​21
​22	​23	​24	​25	​26	​27	​28
​29	​30	​31	​32	​33	​34	​35
36​	​37	​38	​39	​40	​41	​42
​43	​44	​45	​46	​47	​48	​49

Working ​	​	​Square number
​ 1	​1 × 1	​
2	​2 × 2	​
3	​3 × 3	​
​4	​4 × 4	​
​5	​5 × 5	​
​6	​6 × 6	​
​7	​7 × 7	​
8	​8 × 8	​
9	​9 × 9	​
​10	​10 × 10	​
11​	​11 × 11	​

square picture has area 169 cm²

​Find the perimeter of the picture.

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Solution

Find the length of the square,

Find a number which, when multiplied by itself, gives 169.

13 × 13 = 169​

​Perimeter is the distance around the picture. So,

P = 13 cm + 13 cm + 13 cm + 13 cm

= 52 cm

The perimeter of the picture is 52 cm.

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Square Numbers

169cm²​