Math Problem Statement
Which irrational square root is between 8 and 9? (Options: √37, √51, √78, √73)
Solution
The question asks which irrational square root is between 8 and 9. The options given are:
To solve this:
- The number between 8 and 9 is squared to get the range: and .
- So, we need to find a square root of a number between 64 and 81.
Evaluate each option:
- (too small)
- (too small)
- (between 8 and 9)
- (between 8 and 9)
Thus, both and are between 8 and 9. However, based on the question's intent, is a better fit since it's closer to 9.
Answer:
Do you want more details or have any questions?
Related Questions:
- What defines an irrational number?
- How can you approximate square roots manually?
- Why is smaller than 8?
- Can a square root be both rational and irrational?
- How do square roots relate to exponents?
Tip: When solving for square roots, estimate the value by squaring nearby whole numbers to establish a range.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Irrational Numbers
Square Roots
Estimation
Formulas
Square Root Estimation (√n)
Theorems
Irrational Number Properties
Suitable Grade Level
Grades 8-10