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# Practice - Indices and Roots - 07

Welcome, KS3 students to the world of Maths indexing and roots! If you ever wondered what powers and square roots are all about, this fun-filled quiz is for you! Simple indices and roots are not hard to understand once you get going - let’s kick off your adventure with this 10-question quiz. Power up and root down!
1.
What is 16 raised to the power of 0.5?
2
3
4
5
A number raised to the power of 0.5 is the same as taking its square root. So 16 0.5 equals the square root of 16, which is 4.
2.
What is the square root of 64?
6
8
10
12
The square root of a number is the value that, when multiplied by itself, gives the original number. So since 8 x 8 is 64, the square root of 64 is 8.
3.
What is the cube root of 27?
4
5
6
3
The cube root of a number is a value that, when cubed (multiplied by itself twice), gives the original number. So the cube root of 27 is 3, because if you cube 3 (3 x 3 x 3), it equals 27.
4.
What value is represented by 10-1?
1
0.1
-1
10
Negative indices represent the reciprocal of a number. So 10-1 equals 110 which is 0.1.
5.
What is 2 raised to the power of 3 (23)?
4
6
8
10
When a number raised to a power, it is the number multiplied by itself the 'power' times. So 2 cubed (or 23) is 2 x 2 x 2 which equals 8.
6.
Which of the following numbers is irrational?
3
45
2
0.75
Irrational numbers cannot be expressed as a simple fraction and they have never-ending, non-repeating decimal representations. The square root of 2 is irrational.
7.
Which is greater: 25 or 52?
25
52
Both are equal
Neither
25 means multiplying 2 by itself 5 times, which equals 32. While 52 means multiplying 5 by itself 2 times, which equals 25. So, 25 is greater than 52.
8.
Define 40?
0
1
4
Undefined
In maths, anything raised to the power of 0 is always 1. Therefore, 40 equals 1.
9.
What is 1000?
0
1
100
Undefined
Remember, any number raised to the power of 0 is always 1. So, What is 1000 equals 1.
10.
What is the value of 8 to the power 23?
2
4
3
None of the above
When calculating an index that involves fractions, the top number (numerator) is the power and the bottom number (denominator) is the root. So the question is asking for the cube root of 8 squared. The cube root of 8 is 2, and 2 squared is 4.
Author:  Graeme Haw
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