Math Problem Statement

Estimate each square root using perfect squares: √71, √29, √54, √18.

Solution

The problem is asking to estimate each square root using perfect squares. Let's go through each square root estimation based on the perfect squares surrounding the numbers.

  1. √71:

    • The perfect squares around 71 are 64 (√64 = 8) and 81 (√81 = 9).
    • Since 71 is closer to 64, the square root of 71 is a little more than 8.
    • Estimated value: approximately 8.4.
  2. √29:

    • The perfect squares around 29 are 25 (√25 = 5) and 36 (√36 = 6).
    • Since 29 is closer to 25, the square root of 29 is a little more than 5.
    • Estimated value: approximately 5.4.
  3. √54:

    • The perfect squares around 54 are 49 (√49 = 7) and 64 (√64 = 8).
    • Since 54 is closer to 49, the square root of 54 is a little more than 7.
    • Estimated value: approximately 7.3.
  4. √18:

    • The perfect squares around 18 are 16 (√16 = 4) and 25 (√25 = 5).
    • Since 18 is closer to 16, the square root of 18 is a little more than 4.
    • Estimated value: approximately 4.2.

Let me know if you need further details or clarifications!

Here are 5 related questions to expand your understanding:

  1. Can you explain how perfect squares help in estimating square roots?
  2. What is the square root of 50, and how would you estimate it using perfect squares?
  3. How do you know which perfect square a number is closer to?
  4. Why is estimating square roots important in practical situations?
  5. What is the square root of 85, and how can you

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Math Problem Analysis

Mathematical Concepts

Square Roots
Perfect Squares
Estimation

Formulas

Square root approximation using perfect squares: √n ≈ closest lower perfect square + fractional distance.

Theorems

Properties of square roots: If n is not a perfect square, its square root lies between the square roots of the closest perfect squares.

Suitable Grade Level

Grades 6-8