What Is a Square Root?
A number that becomes a when squared is called a square root of a. A positive number has two square roots: one positive and one negative.
Meaning of Square Roots
x² = a means that x is a square root of a.
The square roots of a positive number a are ±√a.
The only square root of 0 is 0.
📘 Example ①
Find the square roots of 9.
Solution: Since 3² = 9 and (−3)² = 9, the square roots of 9 are ±3
Find the square roots of 9.
Solution: Since 3² = 9 and (−3)² = 9, the square roots of 9 are ±3
📘 Example ②
Find the value of √25.
Solution: √25 is the positive square root of 25, so √25 = 5
Find the value of √25.
Solution: √25 is the positive square root of 25, so √25 = 5
💡 Key Points
- √a is the positive square root of a (represented by the radical sign)
- −√a is the negative square root of a
- The square root of a negative number does not exist among the real numbers
Practice Problems
- Find the square roots of 16.
- Find the value of √49.
Answers and Explanations
- Answer: ±4
- Answer: √49 = 7