Page 97 - Knowledge Organiser Yr9 24-25

Knowledge Base: Mathematics Topic 29: Powers and Roots Year 9 | Spring Term, 1st Half
By the end of this topic, you should be able to:
• Find square and cube numbers
• Finding the square and cube roots of numbers
• Write numbers as indices
• Understand the laws of indices
• Simplify surds
• Solve calculations involving surds
Language
Meaning
Example
Square root
The square root of any number is the number which, when multiplied by itself, gives the starting number.
The square roots of 81 is 9 because 9 x 9 is 81.
Cube root
The cube root of any number is the number which, when multiplied by itself and then multiplied by itself again, gives the starting number.
The cube root of 27 is 3 because 3 x 3 x 3 is 27.
Square number
A number that equals a whole number multiplied by itself.
1, 4, 9, 16, 25
1= 1 x 1 , 4= 2 x 2, etc.
Cube number
A number which is found by multiplying an integer by itself three times.
27= 3 x 3 x 3= is the cube of 3.
Index/ power
The index or power tells you how many time to multiply a number itself.
In the index/power is 3. This represents 4 x 4 x 4.
Surd
A root that cannot be written as a whole number or a fraction
Is in surd form = the decimal value cannot be given completely.
Important things to remember:
1) When multiplying numbers involving indices you have to add the indices but when dividing you subtract the indices
2) Before simplifying a surd , look for the factor which is the largest square number
Worked examples
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