3.
If a number is not a rational number, then it is _____. (1 point)
an integer
an irrational number****
A whole number
a radical
4.Mrs. Clarkson designed a rectangular garden with a length of 15 meters and a width of 8 meters. She plans to build a walkway through the garden from one corner to the next. What measure is closest to the length of the diagonal walkway?
8 Meters
11 Meters
17 Meters***
23 Meters
5.Which number is a perfect cube?
5****
100
125
150
6.When adding sqaureroot 25 and -9 which type of number is the sum?
Whole number
Irrational Number
Integer***
Radical
7.What is square root 81/100?
81/100
-9/10
9/10***
8/10
8.Chuck needs to cut a piece of cardboard for an art project at school. He has four pieces of cardboard that he can cut from: 6 inches, 5 inches, 7 inches, and 3 inches. If the length of the cardboard he needs is √35 inches, which piece of cardboard should he cut to create the least amount of unused cardboard?
3 inches
5 inches
6 inches***
7 inches
9. Sylvia made a poster shaped like the triangle shown below.
The hypotenuse is 26in. one like 24 in. and the bottom leg is blank.
What is the length of the third side of the triangle?
10 in****
12 in.
14 in.
16 in.
10.
Four students work to find an estimate for square root 37. Who is closest to finding the true estimate? (1 point)
Rhonda: "Use square root 16 and square root 25 to estimate.
Ricardo: "I use square root 25 and square root 36."
Riley: "It should be between square root 36 and square root 49****
Rhiannon: "Use square root 49 and square root 64 to estimate."
11.Which of these nonterminating decimals can be converted into a rational number? (1 point)
0.626226222...
0.020220222...
0.123123123...****
12.Sam is installing square ceramic tiles on his bathroom floor. The area of each tile is 97 square inches. To the nearest inch, what is the length of one side of the tile?
9 in
10 in****
29 in
49 in
3. To determine what type of number a number is, you need to understand the definition of each type.
- An integer is a whole number that can be either positive, negative, or zero.
- An irrational number is a number that cannot be expressed as a fraction or a decimal because its decimal representation goes on forever without repeating.
- A whole number is a positive integer (including zero).
- A radical is a symbol (like √) used to indicate the square root or other roots of a number.
In this case, if a number is not rational, it means it cannot be expressed as a fraction or a decimal. Therefore, the answer is an irrational number.
4. To find the length of the diagonal walkway in a rectangular garden, you can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the length of the garden is 15 meters and the width is 8 meters. So, the diagonal walkway is the hypotenuse of a right triangle with sides of length 15 and 8.
Using the Pythagorean theorem:
Length of diagonal walkway = √(15^2 + 8^2)
= √(225 + 64)
= √289
≈ 17 meters
Therefore, the measure closest to the length of the diagonal walkway is 17 meters.
5. To determine which number is a perfect cube, you need to understand what a perfect cube is.
A perfect cube is a number that can be expressed as the cube of a whole number. For example, 2^3 = 8, 3^3 = 27, and so on.
In this case, when you calculate the cube root of each number:
- The cube root of 5 is not a whole number, so it is not a perfect cube.
- The cube root of 100 is 4, so it is a perfect cube (4^3 = 64).
- The cube root of 125 is 5, so it is a perfect cube (5^3 = 125).
- The cube root of 150 is not a whole number, so it is not a perfect cube.
Therefore, the number 100 is a perfect cube.
6. When adding √25 and -9, you need to simplify the expression.
√25 is the square root of 25, which is 5.
When adding 5 and -9, the sum is -4.
Therefore, the sum is an integer.
7. To find the square root of 81/100, you need to understand how to simplify square roots of fractions.
You can simplify the square root of a fraction by taking the square root of the numerator and the square root of the denominator separately.
In this case:
- The square root of 81 is 9.
- The square root of 100 is 10.
Therefore, the simplified form of the square root of 81/100 is 9/10.
8. To determine which piece of cardboard Chuck should cut to create the least amount of unused cardboard, you need to compare the length of each piece of cardboard to √35 inches.
Calculating √35 gives an approximate value of 5.92 inches.
- The length of the 3-inch cardboard is too small.
- The length of the 5-inch cardboard is similar to √35 inches, so it is a good choice.
- The length of the 6-inch cardboard is longer than √35 inches, so it would result in unused cardboard.
- The length of the 7-inch cardboard is also longer than √35 inches, so it would result in unused cardboard.
Therefore, Chuck should cut the 5-inch cardboard to create the least amount of unused cardboard.
9. To find the length of the third side of the triangle, you can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the hypotenuse is 26 inches and one leg is 24 inches. Let's call the length of the third side x.
Using the Pythagorean theorem:
26^2 = 24^2 + x^2
676 = 576 + x^2
100 = x^2
Taking the square root of both sides, we get:
√100 = √x^2
10 = x
Therefore, the length of the third side of the triangle is 10 inches.
10. To estimate the square root of 37, you can use the knowledge of square roots of nearby perfect squares.
- Square root 16 is 4, and square root 25 is 5. The estimated square root should be between 4 and 5, so Rhonda's estimate is not the closest.
- Square root 25 is 5, and square root 36 is 6. The estimated square root should be between 5 and 6, so Ricardo's estimate is not the closest.
- Square root 36 is 6, and square root 49 is 7. The estimated square root should be between 6 and 7, so Riley's estimate is the closest.
- Square root 49 is 7, and square root 64 is 8. The estimated square root should be between 7 and 8, so Rhiannon's estimate is not the closest.
Therefore, Riley is closest to finding the true estimate.
11. To determine which nonterminating decimal can be converted into a rational number, you need to know the definition of a rational number.
A rational number is a number that can be expressed as a fraction of two integers.
In this case, the decimal 0.123123123... has a repeating pattern of 123.
To convert it into a fraction, you can set x = 0.123123123... and subtract it from 1000x to eliminate the repeating part:
1000x - x = 123.123123123... - 0.123123123...
999x = 123
x = 123/999
Therefore, the decimal 0.123123123... can be converted into the rational number 123/999.
12. To find the length of one side of the square ceramic tile, you need to calculate the square root of the area of each tile.
Given that the area of each tile is 97 square inches, you need to find the square root of 97.
Calculating √97 gives an approximate value of 9.85 inches.
Rounding to the nearest inch, the length of one side of the tile is 10 inches.
5.Which number is a perfect cube?
5****
100
125
150
ah 125 = 5 * 5 * 5