5 Problems - SHOW ALL WORK!
True or false: the √ 20 is between the integers 4 and 5.
--------------------------------------------------------------------------------
If a square room has a floor with an area of 289 square feet, how long is each side of the floor?
--------------------------------------------------------------------------------
If a square cube has a volume of 729 cubic feet, how long is each side of the cube?
--------------------------------------------------------------------------------
Is the √65 closer to the integer 8 or 9?
--------------------------------------------------------------------------------
Is the fraction ⅓ a repeating or terminating decimal?
1) True or false: the √20 is between the integers 4 and 5.
To solve this, we can determine the square roots of 20, 4, and 5:
√20 ≈ 4.472
√4 = 2
√5 ≈ 2.236
Since √20 is between the values of √4 and √5, the statement is true.
2) If a square room has a floor with an area of 289 square feet, how long is each side of the floor?
To find the length of each side of the floor, we need to find the square root of the area.
√289 = 17
Each side of the square floor is 17 feet long.
3) If a square cube has a volume of 729 cubic feet, how long is each side of the cube?
To find the length of each side of the cube, we need to find the cube root of the volume.
∛729 = 9
Each side of the cube is 9 feet long.
4) Is the √65 closer to the integer 8 or 9?
To determine this, we can find the square roots of 65, 8, and 9:
√65 ≈ 8.062
√8 ≈ 2.828
√9 = 3
Since √65 is closer in value to √9, the integer 9, the answer is 9.
5) Is the fraction ⅓ a repeating or terminating decimal?
To determine this, we can divide 1 by 3:
1 ÷ 3 = 0.33333...
The decimal representation of 1/3 is a repeating decimal, as it repeats the digit 3 indefinitely.
True or false: the √ 20 is between the integers 4 and 5.
4^2 = 16 lowest possible
5^5 = 25 highest possible
so ( 4 +fraction)^2 = 20
To find the fraction that, when added to 4 and squared, equals 20, we can set up the equation:
(4 + fraction)^2 = 20
Expanding and solving, we get:
16 + 8fraction + fraction^2 = 20
Rearranging, we have:
fraction^2 + 8fraction - 4 = 0
Using the quadratic formula, we can solve for the value of the fraction:
fraction = (-b ± √(b^2 - 4ac))/(2a)
where a = 1, b = 8, and c = -4.
Plugging in these values, we get:
fraction = (-8 ± √(8^2 - 4(1)(-4)))/(2(1))
= (-8 ± √(64 + 16))/2
= (-8 ± √80)/2
= (-8 ± √16 * 5)/2
= (-8 ± 4√5)/2
= -4 ± 2√5
Evaluating both possibilities, we have:
fraction ≈ -4 + 2√5 or fraction ≈ -4 - 2√5
Although we have found the exact values for the fraction, the question asks whether the square root of 20 is between 4 and 5. Since we cannot determine exactly where -4 + 2√5 or -4 - 2√5 falls between 4 and 5 without calculating them, we cannot definitively determine whether the square root of 20 is between 4 and 5. Therefore, the answer is indeterminate or inconclusive.