What is the square root of 0?
Or written mathematically:
$$ \sqrt{0} \ ? $$
The square root of 0 is 0.
$$ \sqrt{0} = 0 $$
To learn how you can obtain this answer, let’s explain the concept of a square root first.
What Is A Square Root?
Squaring a number is where you take that number and multiply it by itself:
$$ x \times x = x^2 $$
For example, the square of 2 is 4 — it’s the result of multiplying 2 by 2. Note that the same number is multiplied by itself to form the squared number — this is important.
The opposite of squaring a number is finding the square root.
To find the square root of a number is to find the number that, when multiplied by itself, will equal the number you’ve been asked to find the square root of.
For example, the square root of 4 is 2 because:
$$ \sqrt{4} \ ? \ x \times x = 4 \ 2 \times 2 = 4 $$
To find the square root of 0, we ask what number, when multiplied by itself, gives 0:
$$ \sqrt{0} \ ? \ x \times x = 0 \ 0 \times 0 = 0 $$
Note the important requirement: the same number.
You should know that any number multiplied by 0 equals 0, but in those cases, the numbers may be different. To be a square root, we need to find the same number such that the product equals the target — and in this case, that number is 0.
Square Root Of Zero: Summary
Square roots are often used to solve equations, especially formulas involving squares, such as the Pythagorean theorem. They’re helpful when finding the hypotenuse or other sides in a right-angled triangle.
In this lesson, we saw:
- What it means to square a number
- What a square root is (the inverse of squaring)
- Why the square root of 0 is 0