Math Problem Statement

Which arrow best shows the position of -√5 on the number line?

Solution

To determine which arrow best represents the position of 5-\sqrt{5} on the number line, we first need to approximate the value of 5-\sqrt{5}:

  1. The square root of 5 is approximately 2.24.
  2. Thus, 52.24-\sqrt{5} \approx -2.24.

Looking at the number line, we want the position closest to 2.24-2.24.

The arrows are labeled as follows:

  • Arrow A is located at approximately 3-3,
  • Arrows B and C are near 2-2,
  • Arrow D is around +2+2.

Since 2.24-2.24 is closest to 2-2, the correct answer would be either Arrow B or Arrow C, as they are both positioned around 2-2.

Would you like further explanation on approximating square roots or any other details?

Here are some related questions:

  1. How do you approximate square roots without a calculator?
  2. What is the significance of irrational numbers on a number line?
  3. How do you accurately place irrational numbers on a number line?
  4. Why is 5-\sqrt{5} closer to 2-2 than 3-3?
  5. Can you estimate other roots, like 3\sqrt{3} or 7\sqrt{7}, on a number line?

Tip: To approximate square roots, find two perfect squares closest to the number and estimate between them.

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Math Problem Analysis

Mathematical Concepts

Square Roots
Approximations
Number Line Placement

Formulas

√5 ≈ 2.24

Theorems

-

Suitable Grade Level

Grades 6-8