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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 xx. If we multiply this by itself we get x2x^2. This is the square number.

xx 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 2525 is 55 because we know that 5×5=255 \times 5 = 25

We can denote this with a \sqrt{} sign:


How would you write the following phrase? "Square root of 16"

Multiplying two negatives together gives a positive number. Therefore,2525 has another root:

5×5=25-5 \times -5=25

We can describe the positive and negative square roots with a ±\pm sign - this indicates both a positive and a negative option.

25=±5\sqrt{25}= \pm5


A positive number always has two square roots

A positive and a negative

Find the values of 36\sqrt{36}

Work out the values of 100\sqrt{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=644 \times 4\times4=64

We indicate a cube root with the 3\sqrt[3]{}symbol.


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:



A number only has one cube root

But it can be either POSITIVE or NEGATIVE

What is the cube root of 2727?

Work out the value of 1253\sqrt[3]{125}.

The square root of 0 is 0. This is because: 0×0=00 \times 0 = 0