Let's break down the two practice problems from the image you uploaded:

1. A square has an area of 81 square feet. Select all expressions that equal the side length of the square, in feet.

• To solve this, we need to recall that the area of a square is given by $A = s^2$, where $s$ is the side length.

• If the area is 81 square feet, we can find the side length by solving:

  $s^2 = 81$

• Taking the square root of both sides:

  $s = \sqrt{81} = 9$

So, the side length of the square is 9 feet. Now, select all the expressions that equal 9.

• A: $\sqrt{81}$ = 9 → Correct.
• B: $\sqrt{9}$ = 3 → Incorrect.
• C: $\sqrt{81} \div 2$ = 9/2 = 4.5 → Incorrect.
• D: $\sqrt{64}$ = 8 → Incorrect.
• E: 9 → Correct.

2. Write the exact value of the side length, in units, of a square whose area is:

We'll address each sub-question individually.

• a) 9.25 square units:
  Using the formula $s = \sqrt{A}$, where $A$ is the area,
  $s = \sqrt{9.25}$. Using a calculator:

  $s \approx 3.041$

  So, the side length is approximately 3.041 units.

• b) 37 square units:
  $s = \sqrt{37}$:

  $s \approx 6.083$

  So, the side length is approximately 6.083 units.

• c) 7 square units:
  $s = \sqrt{7}$:

  $s \approx 2.646$

  So, the side length is approximately 2.646 units.

• d) 0.0001 square units:
  $s = \sqrt{0.0001}$:

  $s = 0.01$

  So, the side length is exactly 0.01 units.

Let me know if you'd like further details or clarification!

Related Questions:

1. What is the side length of a square with an area of 100 square units?
2. How do you find the side length of a rectangle if only the area is given?
3. What are some real-life applications of square root calculations?
4. Can you explain how to simplify square roots?
5. What is the relationship between the perimeter and area of a square?

Tip:

Always remember that when finding the side length of a square, you must take the positive square root since side lengths are always positive!