Introduction
Powers
are used when we want to multiply a number by itself repeatedly.
1. Powers
When we
wish to multiply a number by itself we use powers.
For
example, the quantity 74= 7 × 7 × 7 × 7 is usually written as 74. The
number 4 tells us the number of sevens to be multiplied together. In this
example, the exponent, or index, is 4. The number 7 is called
the base.
Example
62
= 6 · 6 = 36. We say that ‘6 squared is 36’, or ‘6 to the power of 2 is 36’.
43
= 4 · 4 · 4 = 64. We say that “4 cubed is 64”, or “4 to the power of 3 is 64”
25
= 2× 2 × 2 × 2 × 2 = 32. We say that ‘2 to the power of 5 is 32’.
Most
calculators have a button marked xy, or simply ˆ to
calculate a power. Ensure that you are using the calculator correctly by
verifying that
75
= 16807.
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- Square roots
When 5
is squared we obtain 25. That is 52 = 25.
The
reverse of this process is called finding a square root. The square root of 25 is 5. This is
written as
 5
Note
also that when −5 is squared we again obtain 25, that is (-5)2= 25. This means that 25 has another square root, −5.
In
general, a square root of a number is a number which when squared gives the
original number.
There
are always two square roots of any positive number, one positive and one
negative.
Therefore,
negative numbers do not possess any square roots.
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- Perfect squares
| A square number, also
called a perfect square, is an integer that is the square of another
integer. In other words, it is the product of some integer with itself. So, for example, 9 is a square number, since it can be written as 32 |
- Cube roots and higher roots
The
cube root of a number, is the number which when cubed gives the original
number.
both
positive and negative, possess a single cube root.
Higher
roots are defined in a similar way: because 25 = 32, the fifth root
of 32 is 2.
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. All numbers,EJERCICIOS
Potencias
Repaso potencias y raices
Operaciones combinadas