Square Roots
Estimate the following square roots by bounding them by consecutive integers. State which integer they
are closest to.
1. 42
between 6 and 7, closer to 6
2. 66
between 8 and 9, closer to 8
3. 131
between 11 and 12, closer to 11
4. 10,051
between 100 and 101, closer to 100
5. 96
between 9 and 10, closer to 10
Solve the following problems:
6. Sue’s first grade class is decorating greeting cards. She has papers that are 6 inch by 8 inch
rectangles. She wants to put a piece of ribbon along the diagonal of each. How long does that
ribbon have to be?
The diagonal is the hypotenuse of a right triangle: a2 + b2 = c2
(6)(6) + (8)(8) = 36 + 64 = 100 = c2
the diagonal is the square root of 100 or 10
7. Billy Joe divided his rectangular pasture in half with a diagonal fence. Somewhere along the line
he forgot the length of one side, and since it has been raining, he doesn’t want to go measure it.
He remembers that the shortest side was 5 feet long. The diagonal fence he added is 13 feet
long. How long is the third side? What is the area of the triangular pasture?
The diagonal is the hypotenuse of a right triangle: a2 + b2 = c2
b2 = c2 - a2 or (13)(13) – (5)(5) = 169 – 25 = 144, b2 = 144 or b = 12
The two legs of the triangle are 5 and 12, the base and the height
the Area = ½ bh = ½ (12)(5) = 30 square feet
8. Mark created the shape below during metal shop by cutting a rectangular piece of metal in half,
diagonally, then punching a circle out of one of the triangles. The diagonal cut was 10 inches
long, one side of the original rectangle was 6 inches, and the diameter of the circle is 3 inches.
The metal weighs one oz. for every square inch of surface area. How much does his resulting
shape, the triangle less the circle, weigh?
Need the base of the triangle: use the Pythagorean them, 36 + x2 = 100, x2 = 64, x = 8.
The area is 6 x 8 = 48 inches. The area of the circle is r2, where r = 1.5, A= 2.25.
The shaded area is 48 – 2.25 square inches, which is the weight