Math Problem Statement

Find two consecutive whole numbers that \(\sqrt{28}\) lies between.

Solution

To determine the two consecutive whole numbers that 28\sqrt{28} lies between, we can calculate:

  1. Find the square roots of two perfect squares closest to 28:

    • 52=255^2 = 25
    • 62=366^2 = 36
  2. Therefore, 28\sqrt{28} lies between 25\sqrt{25} and 36\sqrt{36}.

  3. Simplifying, 28\sqrt{28} lies between 5 and 6.

Answer: 28\sqrt{28} is between 5 and 6.

Let me know if you'd like further details or have any questions.

Here are 5 related questions for deeper understanding:

  1. What is the approximate decimal value of 28\sqrt{28}?
  2. How can you estimate square roots of non-perfect squares without a calculator?
  3. Why does 28\sqrt{28} lie between 25\sqrt{25} and 36\sqrt{36}?
  4. How would you compute 28\sqrt{28} exactly in simplified radical form?
  5. Can you think of another method to find consecutive integers for a square root?

Tip: Always compare the given number with the squares of integers to find its position on the number line.

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Math Problem Analysis

Mathematical Concepts

Square Roots
Inequalities
Number Sense

Formulas

\(a^2 < x < b^2 \implies a < \sqrt{x} < b\)

Theorems

Square Root Property

Suitable Grade Level

Grades 5-7