We will learn how to compare numbers containing radicals and how to find approximate values of square roots.
How to Compare Values
For positive numbers a and b, if a < b, then √a < √b.
When comparing an integer with a number containing a radical, rewrite the integer in radical form.
📘 Example ①
Compare √5 and 2.
Solution: Since 2 = √4 and √4 < √5, 2 < √5
Compare √5 and 2.
Solution: Since 2 = √4 and √4 < √5, 2 < √5
📘 Example ②
Find the approximate value of √2 to the second decimal place (√2 ≈ 1.41421…).
Solution: √2 ≈ 1.41
Find the approximate value of √2 to the second decimal place (√2 ≈ 1.41421…).
Solution: √2 ≈ 1.41
💡 Key Points
- Compare values using the numbers inside the radicals (the greater the number inside, the greater the value)
- √2 ≈ 1.414, √3 ≈ 1.732, and √5 ≈ 2.236 are commonly used approximate values
- Understand that approximate values contain error
Practice Problems
- Compare √7 and 3.
- Find the approximate value of √3 to the second decimal place (√3 ≈ 1.732).
Answers and Explanations
- Answer: Since 3 = √9 and √7 < √9, √7 < 3
- Answer: √3 ≈ 1.73