Square Roots Examples in Math
Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Square Roots.
This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.
Concept Recap
The square root of a number a is the non-negative value b such that b \times b = a; it is the inverse of squaring and is written \sqrt{a}. For example, \sqrt{25} = 5 because 5^2 = 25.
\sqrt{25} asks: what number times itself equals 25? Answer: 5.
Read the full concept explanation →How to Use These Examples
- Read the first worked example with the solution open so the structure is clear.
- Try the practice problems before revealing each solution.
- Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea: Square root is the inverse of squaring—finding the original from the result.
Common stuck point: Not all square roots are nice integers (\sqrt{2} \approx 1.414\ldots).
Sense of Study hint: Ask yourself: what number times itself gives this value? Test a few perfect squares to build intuition.
Worked Examples
Example 1
easySolution
- 1 Recall that a square root asks for the positive number whose square equals the original number.
- 2 Ask: what number multiplied by itself gives 144?
- 3 Test: 12 \times 12 = 144. So \sqrt{144} = 12.
Answer
Example 2
mediumPractice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
mediumExample 2
easyRelated Concepts
Background Knowledge
These ideas may be useful before you work through the harder examples.