Square Roots Formula
Square roots are the non-negative number b such that b^2 = a, written √a = b — the inverse of squaring.
The Formula
When to use: asks: what number times itself equals 25? Answer: 5.
Quick Example
Notation
What This Formula Means
The non-negative number such that , written — the inverse of squaring.
asks: what number times itself equals 25? Answer: 5.
Formal View
Worked Examples
Example 1
easyAnswer
First step
Full solution
- 2 Ask: what number multiplied by itself gives 144?
- 3 Test: . So .
Example 2
mediumExample 3
mediumCommon Mistakes
- Dividing by 2 instead of finding a self-product — , not 18.
- Forgetting non-perfect squares need estimates or radical form — is not a tidy decimal.
- Ignoring the principal root convention — means 6, even though .
Why This Formula Matters
Square roots connect exponents, area, the Pythagorean theorem, distance, and irrational numbers. Recognizing roots as inverse squares prevents calculator-only thinking. Recognizing it by "What number multiplied by itself gives the radicand?" — rather than by familiar numbers — is what lets a student tell it apart from cube roots and exponents in a mixed problem set.
Frequently Asked Questions
What is the Square Roots formula?
The non-negative number such that , written — the inverse of squaring.
How do you use the Square Roots formula?
asks: what number times itself equals 25? Answer: 5.
What do the symbols mean in the Square Roots formula?
The principal square root is the nonnegative number whose square is the radicand.
Why is the Square Roots formula important in Math?
Square roots connect exponents, area, the Pythagorean theorem, distance, and irrational numbers. Recognizing roots as inverse squares prevents calculator-only thinking. Recognizing it by "What number multiplied by itself gives the radicand?" — rather than by familiar numbers — is what lets a student tell it apart from cube roots and exponents in a mixed problem set.
What do students get wrong about Square Roots?
The procedure for square roots is the easy part; the trap is dividing by 2 instead of finding a self-product. Asking "What number multiplied by itself gives the radicand?" first is what keeps a correct-looking calculation from being attached to the wrong concept.
What should I learn before the Square Roots formula?
Before studying the Square Roots formula, you should understand: exponents, multiplication.
Want the Full Guide?
This formula is covered in depth in our complete guide:
Cube Roots, Square Roots, and Irrational Numbers →