YOU ARE LEARNING:
Roots
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Roots
The root of a number is a number which, when multiplied by itself, will make the original number.
Roots reverse the process of indices, to find the original number.
Imagine a number, let's call it x. If we multiply this by itself we get x2. This is the square number.
x would be the square root as it is the number that was originally squared.
What is a square root?
Let's think about this concept with numbers.
The square root of 25 is 5 because we know that 5×5=25
We can denote this with a sign:
25=5
How would you write the following phrase? "Square root of 16"
Multiplying two negatives together gives a positive number. Therefore,25 has another root:
−5×−5=25
We can describe the positive and negative square roots with a ± sign - this indicates both a positive and a negative option.
25=±5
A positive number always has two square roots
A positive and a negative
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/o8KHwOMnQA2iLDq1IXNh.png)
Find the values of 36
Work out the values of 100
A cube root of a number is a number which, when multiplied by itself 3 times, generates the original number. The cube root of 64 is 4.
4×4×4=64
We indicate a cube root with the 3symbol.
364=4
How would you write "the cube root of 125"?
Unlike square roots, a number will only have one cube root, but we can consider positive and negative numbers. For example:
3−8=−2
A number only has one cube root
But it can be either POSITIVE or NEGATIVE
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/k4ZJzlbiS7yyMLr6M55d.png)
What is the cube root of 27?
Work out the value of 3125.
The square root of 0 is 0. This is because: 0×0=0