Squares and square roots

The Maths Habit

How many small squares?

5 × 2 = 10
4 × 3 = 12
3 × 3 = 9

Which of these are squares? How do you know?

ASquare
BNot a square
CSquare
DNot a square

A square has the same number along as up.

Area
The space inside a flat shape.
sidesidearea
Squared
A number multiplied by itself. The small ² means squared.
Square number
The answer when a whole number is squared.
areasideside
Square root
The number that was squared. The sign is √.

sidesidearea
side×side=area
side2=area
  1. 1Label the square.Write the side on two sides.
  2. 2Side × side.Multiply the side by itself. The small ² does not mean × 2.
  3. 3Write the answer.This is the area. It is a square number.

Work out 32.

1Label the square.
339
2Side × side.
3×3=9
3Write the answer.
32 =9

Work out 52.

1Label the square.
5525
2Side × side.
5×5=25
3Write the answer.
52 =25

Work out 32.

1Label the square.
339
2Side × side.
3×3=9
3Write the answer.
32 =9
1sidesidearea2side×side=area3side2=area

Work out 102.

1Label the square.
1010100
2Side × side.
10×10=100
3Write the answer.
102 =100

Work out 32.

1Label the square.
339
2Side × side.
3×3=9
3Write the answer.
32 =9
1sidesidearea2side×side=area3side2=area

Work out 42.

1Label the square.
4416
2Side × side.
4×4=16
3Write the answer.
42 =16

Work out 32.

1Label the square.
339
2Side × side.
3×3=9
3Write the answer.
32 =9
1sidesidearea2side×side=area3side2=area

Work out 62.

1Label the square.
6636
2Side × side.
6×6=36
3Write the answer.
62 =36

1sidesidearea2side×side=area3side2=area

1Work out 72.

1
7749
2
7×7=49
3
72 =49

2Work out 92.

1
9981
2
9×9=81
3
92 =81

3A square stamp has sides of 8 cm. Work out its area.

1
8 cm8 cm64 cm2
2
8×8=64
3
Area =64cm²

Copy and finish the square numbers.

Side12345678910Side × side149162536496481100

areasideside
side×side=area
√area=side
  1. 1Label the square.Write the area in the middle.
  2. 2Side × side.Which number times itself makes the area?
  3. 3Write the answer.The side is the square root.

Work out √16.

1Label the square.
16??44
2Side × side.
4×4=16
3Write the answer.
√16 =4

Work out √25.

1Label the square.
25??55
2Side × side.
5×5=25
3Write the answer.
√25 =5

Work out √16.

1Label the square.
16??44
2Side × side.
4×4=16
3Write the answer.
√16 =4
1areasideside2side×side=area3√area=side

Work out √100.

1Label the square.
100??1010
2Side × side.
10×10=100
3Write the answer.
√100 =10

Work out √16.

1Label the square.
16??44
2Side × side.
4×4=16
3Write the answer.
√16 =4
1areasideside2side×side=area3√area=side

Work out √9.

1Label the square.
9??33
2Side × side.
3×3=9
3Write the answer.
√9 =3

Work out √16.

1Label the square.
16??44
2Side × side.
4×4=16
3Write the answer.
√16 =4
1areasideside2side×side=area3√area=side

Work out √49.

1Label the square.
49??77
2Side × side.
7×7=49
3Write the answer.
√49 =7

1areasideside2side×side=area3√area=side

1Work out √36.

1
36??66
2
6×6=36
3
√36 =6

2Work out √81.

1
81??99
2
9×9=81
3
√81 =9

3A square playground has an area of 64 m². How long is each side?

1
64 m2??88
2
8×8=64
3
Side =8m

Is it right?
Thumbs up: right. Thumbs down: wrong.

  1. 62 = 12

    Wrong: 6 × 6 = 36

  2. √49 = 7

    Right: 7 × 7 = 49

  3. 102 = 100

    Right

  4. √16 = 8

    Wrong: 4 × 4 = 16

  5. 32 = 9

    Right

Squares and square roots worksheet, page 1

Squares and square roots worksheet, page 2

Answer sheet

  1. Find two square numbers that add up to 13.

    4 and 9

  2. A square has an area of 36 cm². Work out its perimeter.

    24 cm

  3. √30 is between two whole numbers. Which two?

    5 and 6

  1. Work out 62.

    36
    1Label thesquare.662Side × side.×=3Write theanswer.62 =

  2. Work out √81.

    9
    1Label thesquare.??2Side × side.×=3Write theanswer.√81 =

  3. A square has an area of 16 cm². How long is each side?

    4 cm
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