Math Problem Statement

If the area of a square is 32 square feet, estimate the length of each side of the square to the nearest whole number.

Solution

The area AA of a square is given by the formula:

A=s2A = s^2

where ss is the length of one side of the square.

Given that the area is 32 square feet, we can set up the equation:

s2=32s^2 = 32

To find the side length, take the square root of both sides:

s=32s = \sqrt{32}

Estimating 32\sqrt{32}, we get approximately:

s5.656s \approx 5.656

Rounding this to the nearest whole number, the length of each side of the square is approximately 6 feet.

Would you like further details or have any questions?

Here are 5 related questions you might find interesting:

  1. What is the perimeter of this square?
  2. If the side length were doubled, what would the new area be?
  3. How does the diagonal of a square relate to its side length?
  4. What is the side length if the area is 50 square feet?
  5. Can you calculate the exact value of 32\sqrt{32} in simplest radical form?

Tip: When estimating square roots, it's helpful to know squares of nearby numbers, like 52=255^2 = 25 and 62=366^2 = 36.

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Math Problem Analysis

Mathematical Concepts

Geometry
Square Roots
Area of a Square

Formulas

A = s^2
s = √A

Theorems

Pythagorean Theorem (for square root estimation)

Suitable Grade Level

Grades 6-8