Understand and learn the words: square, positive and negative square root, cube and cube root, learn squares up to 15x15 and cubes up to 5 cubed
Square numbers
'Squaring' a number is essentially multiplying it by itself.
2^{2} means '2 squared', or 2 x 2.
The small ^{2} is an index number, or power. It tells us how many times we should multiply 2 by itself.
Similarly 5^{2} means '5 squared’ or 5 x 5.
And 10^{2} means '10 squared', or 10 x 10.
So, 1^{2} = 1 x 1 = 1
2^{2} = 2 x 2 = 4
3^{2} = 3 x 3 = 9
4^{2} = 4 x 4 = 16
5^{2} = 5 x 5 = 25
The square numbers can be written in a sequence:
1, 4, 9, 16, 25… are known as square numbers.
Square roots
The opposite of a square number is a square root.
We use this symbol √ to mean square root.
So we can say that √4 = 2 and √25 = 5.
However, this is not the whole story, because 2 x 2 is also 4, and 5 x 5 is also 25.
So, in fact, √4 = 2 or 2. And √25 = 5 or 5.
The square root can also be shown as an index number of 1/2.
Cube numbers
2^{3} simply means ‘2 cubed’ or 2x2x2.
The cubed symbol, ^{‘3’}, tells us how many times to multiply the number its attached to.
So, 3^{3} means 3x3x3
1^{3}^{ }means 1x1x1 = 1
2^{3 }means 2x2x2 = 8
3^{3 }means^{ }3x3x3 = 27
4^{3 }means 4x4x4 = 64
Cube roots
The opposite of a cube number is a cube root. We use the symbol to mean cube root. Each number only has only one cube root, unlike square roots which can have both positive and negative versions of the same number.
Similar to square roots, cubed roots can also be shown with an index number 1/3, as an alternative to the symbol.
Examples:
^{3}√8 = 2
^{3}√27 = 3
^{3}√64 = 4
^{3}√125 = 5
Squares upto 15x15
· 1^{2} = 1 x 1 = 1
· 2^{2} = 2 x 2 = 4
· 3^{2} = 3 x 3 = 9
· 4^{2} = 4 x 4 = 16
· 5^{2} = 5 x 5 = 25
· 6^{2} = 6 x 6 = 36
· 7^{2} = 7 x 7 = 49
· 8^{2} = 8 x 8 = 64
· 9^{2} = 9 x 9 = 81
· 10^{2} = 10 x 10 = 100
· 11^{2} = 11 x 11 = 121
· 12^{2} = 12 x 12 = 144
· 13^{2} = 13 x 13 = 169
· 14^{2} = 14 x 14 = 196
· 15^{2} = 15 x 15 = 225
Cubes upto 5
· 1^{3} = 1 x 1 x 1 = 1
· 2^{3} = 2 x 2 x 2 = 8
· 3^{3} = 3 x 3 x 3 = 27
· 4^{3} = 4 x 4 x 4 = 64
· 5^{3} = 5 x 5 x 5 = 125
Follow the links below to see how this topic has appeared in past exam papers
AQA Unit 2 June 2011 (F)  Page 2, Question 1(e)
AQA Unit 2 June 2011 (F)  Page 6, Question 8(a)
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