Math Problem Statement

Circle the correct answer for each question and find the side length of the square given its area.

Solution

Let's solve the questions shown in the image.

1. Circle the correct answer for each question:

a) 9\sqrt{9}
9=3\sqrt{9} = 3
So, the correct answer is 3.

b) 16216^2 162=25616^2 = 256
The correct answer is 256.

c) 100\sqrt{100} 100=10\sqrt{100} = 10
The correct answer is 10.

d) 36\sqrt{36} 36=6\sqrt{36} = 6
The correct answer is 6.

e) 25225^2 252=62525^2 = 625
The correct answer is 625.


2. The area, AA, of a square is given. Find the side length of the square.

The area of a square is calculated as A=s2A = s^2, where ss is the side length. We need to find ss for each given area:

a) A=50cm2A = 50 \, \text{cm}^2
s=507.07cms = \sqrt{50} \approx 7.07 \, \text{cm}

b) A=8mm2A = 8 \, \text{mm}^2
s=82.83mms = \sqrt{8} \approx 2.83 \, \text{mm}

c) A=169cm2A = 169 \, \text{cm}^2
s=169=13cms = \sqrt{169} = 13 \, \text{cm}

Would you like further details on any of these solutions?


5 Related Questions:

  1. How do you calculate the square root of a number?
  2. What is the formula for the area of a square?
  3. Can a square have negative side lengths?
  4. What are the units of area and how do they relate to side lengths?
  5. How can the square root of non-perfect squares be estimated?

Tip: For any square's area, the side length is always the square root of the area.

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Math Problem Analysis

Mathematical Concepts

Square Roots
Exponents
Area of a Square

Formulas

Square root: \(\sqrt{x}\)
Exponentiation: \(x^2\)
Area of a square: \(A = s^2\)

Theorems

The square root property
Area of squares

Suitable Grade Level

Grades 6-8