Math Problem Statement

Determine which two values the following number is between: √11

Solution

The question asks to determine which two values the square root of 11 (11\sqrt{11}) is between.

Let's calculate 11\sqrt{11}:

113.3166\sqrt{11} \approx 3.3166

Now, we compare this value to the options provided:

  • A. 3.29 and 3.3
  • B. 3.3 and 3.31
  • C. 3.31 and 3.32
  • D. 3.32 and 3.33

Since 3.31663.3166 lies between 3.31 and 3.32, the correct answer is C. 3.31 and 3.32.

Would you like further details or explanations?

Here are 5 related questions you could explore:

  1. What is the square root of 12, and which range does it fall between?
  2. How can you estimate square roots without a calculator?
  3. What is the decimal approximation of 50\sqrt{50}?
  4. How do square roots behave for numbers between perfect squares?
  5. Why does the square root of 11 result in an irrational number?

Tip: When estimating square roots, find the nearest perfect squares for an approximation.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Square Roots
Number Comparison

Formulas

Square Root Approximation

Theorems

Irrational Numbers

Suitable Grade Level

Grades 6-8