Square Roots Worksheet
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1
2Square Roots
The square root of a number is a value that, when multiplied by itself, gives the number.
index
radicand
radical sign
Examples of the first 12 square roots and cube roots (they are endless):
Square Roots
Cube Roots
3
1x1
1
1
1
1x1x1
1
1
1
3
2x2
4
4
2
2x2x2
8
8
2
3
3x3
9
9
3
3x3x3
27
27
3
3
4x4
16
16
4
4x4x4
64
64
4
3
5x5
25
25
5
5x5x5
125
125
5
3
6x6
36
36
6
6x6x6
216
216
6
3
7x7
49
49
7
7x7x7
343
343
7
3
8x8
64
64
8
8x8x8
512
512
8
3
9x9
81
81
9
9x9x9
729
729
9
3
10x10 100
100 10
10x10x10 1000
1000 10
3
11x11 121
121 11
11x11x11 1331
1331 11
3
12x12 144
144 12
12x12x12 1728
1728 12
th
th
th
There are many different roots, 4
, 5
, 6
, etc. They all follow the same rules.
Many times you are asked to find the square root of a number without using a calculator. That means an
answer will not contain a decimal answer. To find the square root without using a calculator, try to
break the number down into a perfect square and another number. The “perfect square” comes out and
the other number stays under the radical sign.
40
4
10
2
10
The “perfect square” is brought outside the radical and the rest
of the number stays under the radical sign because it is not a
50
25 2
5 2
perfect square.
1
1
4
2
9
3
1
1
100
10
81
9
25
5
121
11
Cube roots – think of three of the same numbers, when multiplied together, give you the number.
3
3
3
8
2 2 2
2
27
3 3 3 3
8
2
2
2
2
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