Square root
- CBSE · NCERT Class 8 Part 1, Ch 1 A Square and A Cube
A square root of a number is a value that, multiplied by itself, gives that number, so a square root of 49 is 7.
Squaring and square roots undo each other. 7 squared is 7 × 7 = 49, so 7 is a square root of 49. The sign √ is used for the positive root, so √49 = 7.
There is a second root. (-7) × (-7) is also 49, so -7 is a square root of 49 as well. When both are meant, we write ±7. Numbers like 1, 4, 9, 16 and 25 are perfect squares. Their square roots are whole numbers.
A small example
Find √784 using prime factors. 784 = 2 × 2 × 2 × 2 × 7 × 7. Make pairs: (2 × 2), (2 × 2), (7 × 7). Take one number from each pair: 2 × 2 × 7 = 28. So √784 = 28.
If a prime is left without a partner, the number is not a perfect square. 50 = 2 × 5 × 5 leaves a single 2. So √50 is not a whole number. It equals 5√2.
Why it matters later
In Class 10 Chapter 1 you prove that √2 and √3 are irrational. In Chapter 4, the quadratic formula has a square root at its heart. Remembering that a square root can be positive or negative is what gives a quadratic its two roots.
Sources
Facts last checked against these sources on 30 September 2026.
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