Michelle is measuring the dimensions of her living room so she can install new flooring. She measures the length at 4√12 feet with her radical tape measure, and then measures the width at 3√8 feet.

Question

Michelle is measuring the dimensions of her living room so she can install new flooring. She measures the length at 4√12 feet with her radical tape measure, and then measures the width at 3√8 feet.

1. Determine the area of the living room. Leave your answer as a simplified radical expression and include units.

2. Michelle decided she only wants to cover ¾ of the room in the new flooring. Determine the area of flooring she will need to cover ¾ of the room. Leave your answer as a simplified radical expression and include units.

3. For the remaining portion of the living room not covered by the new flooring, Michelle wants to paint the concrete. After carefully measuring the exposed concrete, she determines 6 square feet are already painted and the remaining unpainted area forms a square with side length x. The entire area of concrete, including the painted and unpainted portions, is a total of 31 square feet. Write an equation that could be used to find the unpainted square side length x.

4. After installing the new flooring, Michelle plans to install new baseboards around the perimeter of the room. Help Michelle by determining the perimeter of the room, leaving your answer as a simplified radical expression.

Answer 1

1,2 and 4 are similar to the answer above. 3 can be looked at in a simple way. Total area is 31^{2 feet and the painted area is} 6^{2 feet so the unpainted area is} 5^{2 feet. This the questions points out happens to be a square and since area of a square is side squared or side mutliplied by side; side of the square would be simply 5.}

Answer 2

You can start by simplifying the radical expressions:

4√12 = 4√4√3 = 8√3

3√8 = 3√4√2 =6√2

you can always write √(a*b) as √a*√b, or vice versa

Give the calculations a go and see where you get.