radicals word problems

Question

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.

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. 5. When Michelle goes to the local hardware store to purchase the baseboards, the shop owner tells her his conversion calculator is broken and he only has 14 yards of baseboard in stock. Help Michelle by converting the perimeter to yards and determine if the hardware store has enough baseboard for her room. Hint: 3 feet are in 1 yard.

Answer 1

(1)   4*sqrt(12)  x 3*sqrt(8) = 4 * sqrt(2*2*3) x 3 * sqrt(2*2*2) = 4 * 2 * sqrt(3) x 3 * 2 * sqrt(3)

                                                                                            = 4 *2 * 3 * 2 * 3 = 144

       The area is 144 square feet

 

(2)  As in the previous problem.  X^2 + 6 = 31

                                                 x^2  = 25 <--- subtracts 6 from both sides

                                                  x = +or- 6  <--- takes square root of both sides.

      The measurement must be positive, so 5 feet

 

(3) the perimeter is 2 * 4 *sqrt(12) + 2 * 3 * sqrt(8) = 8 * sqrt(12) + 6 * sqrt(8)

                                                                    

                                                                              = 8 * 2 * sqrt(3) + 6 * 2 * sqrt(2)

 

                                                                             = 16*Sqrt(3) + 12 * sqrt(2) = 44.68 feet

 

(4) 44.68 feet /3 feet per yard = 14.8944... yards

     she will need 2 of the 14 yard baseboards but will only use less than

      1 yard of the second piece.