What is a Square Root?
A square root is the inverse of squaring — a core concept in Grade 8 math (Yoshiwara Core Math). The square root of n is the value that, when multiplied by itself, equals n. Written √n, it gives the side length when n is the area of a square. Perfect squares 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 have whole-number roots. Non-perfect squares like √2 are irrational numbers. Square roots are essential for solving quadratic equations, applying the Pythagorean theorem, and geometry area problems.
Key Concepts
Property A number $s$ is called a square root of $N$ if $s^2 = N$. We use a special symbol called a radical sign, $\sqrt{\hphantom{0}}$, to denote the positive square root of a number. For example, $\sqrt{16}$ means "the positive square root of 16," so $\sqrt{16} = 4$. Numbers such as 16 and 25 are called perfect squares because they are the squares of whole numbers.
Examples 4 is a square root of 16 because $4^2 = 16$. 9 is a square root of 81 because $9^2 = 81$. $\frac{3}{5}$ is a square root of $\frac{9}{25}$ because $(\frac{3}{5})^2 = \frac{9}{25}$.
Explanation Think of a square root as the reverse of squaring a number. If you know the area of a square, the square root tells you the length of its side. It answers the question: "What number, when multiplied by itself, gives this result?".
Common Questions
What is the definition of a square root?
The square root of n is the value that multiplied by itself gives n. Written as √n, it is the inverse of squaring.
What are the perfect squares up to 100?
1, 4, 9, 16, 25, 36, 49, 64, 81, 100. Their square roots are 1–10 respectively.
What is the difference between perfect and non-perfect square roots?
Perfect squares have exact whole-number roots. Non-perfect squares produce irrational (non-terminating) decimal roots.
How does square root relate to square area?
If a square has area A, its side length = √A. A square with area 49 cm² has side 7 cm.
How is the square root symbol written?
The symbol is √. √36 is read 'the square root of 36' and equals 6.