Glossary
square root
A square root is the number that, multiplied by itself, gives the value you started with: the square root of 49 is 7, because 7 × 7 = 49.
A square root is the number which, multiplied by itself, produces the given value. The square root of 49 is 7 because 7 × 7 = 49, and the square root of 144 is 12 because 12 × 12 = 144. It is the reverse of squaring a number, and taking a root is the opposite operation to raising a power — which is why a root and an exponent are usually taught together.
Perfect squares are worth memorizing: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121 and 144, with their roots 1 through 12. Most ASVAB root questions draw on that list. When a value is not a perfect square, estimate between the two nearest ones — the square root of 50 is a little above 7, since 49 is 7² and 64 is 8² — and a fraction such as 1/4 has a root too, since 1/2 × 1/2 = 1/4.
The most common slip is forgetting that squaring a number and doubling it are different: 6² is 36, not 12. Roots also turn up inside geometry formulas, which is why the Pythagorean theorem always ends in a square root.
Taught in
Related terms
- exponent — An exponent tells you how many times to multiply a number by itself: 2 to the third power means 2 × 2 × 2. It is shorthand for repeated multiplication.
- Pythagorean theorem — The Pythagorean theorem states that in a right triangle, a² + b² = c², where c is the hypotenuse. It finds a missing side whenever two are known.
Source: Official ASVAB — subtest descriptions (what each subtest asks) and the CAT-ASVAB scored-question counts (accessed 2026-09)