Which of the following is a rational number:
√32 , √81 , √90 , √125
√32 is not a rational number as it is an irrational number.
√81 is a rational number as it equals 9, which is a whole number.
√90 is not a rational number as it is an irrational number.
√125 is not a rational number as it is an irrational number.
The circumference of a circle equals pi times the diameter. Using 3.14 to approximate pi, what is the approximate circumference in inches of a circle with a diameter of 1/2 in.?
To find the approximate circumference, we use the formula:
C = pi * d
where C is the circumference and d is the diameter.
Given that the diameter is 1/2 inch and using 3.14 as an approximation for pi, we can substitute the values into the formula:
C = 3.14 * (1/2)
C = 1.57 inches
Therefore, the approximate circumference of a circle with a diameter of 1/2 inch is 1.57 inches.
9/4 is close to the square root of what integer?
To find an integer that is close to the square root of 9/4, we can calculate the square root of 9/4:
√(9/4) = √9 / √4 = 3/2
So, the integer that is close to the square root of 9/4 is 3.
To determine which of the given numbers are rational, we need to determine whether they can be expressed as a fraction of two integers.
1. √32: This can be simplified as √(16 × 2) = √16 × √2 = 4√2. Since √2 is an irrational number, the whole expression is also irrational.
2. √81: This is equal to 9, which is a rational number.
3. √90: This can be simplified as √(9 × 10) = √9 × √10 = 3√10. Since √10 is an irrational number, the whole expression is irrational.
4. √125: This is equal to 5√5. Since √5 is an irrational number, the whole expression is irrational.
Therefore, the only rational number among the given options is √81.
To determine which of the numbers given are rational numbers, we first need to understand what rational numbers are. Rational numbers are numbers that can be expressed as a fraction of two integers, where the denominator is not zero.
To determine if a given number is rational or not, we can check if the number can be written in the form √n, where n is a positive integer. If we can simplify the square root of a number to an integer or a fraction, then it is rational.
Let's check each of the given numbers:
1. √32: To determine if √32 is rational, we need to simplify it. We can rewrite 32 as 16 * 2. Since the square root of 16 is 4, we can simplify √32 as 4√2. Since √2 cannot be simplified further, this number is not rational.
2. √81: To determine if √81 is rational, we can simplify it. The square root of 81 is 9. Since 9 is an integer, √81 can also be expressed as the fraction 9/1. Therefore, √81 is a rational number.
3. √90: To determine if √90 is rational, we need to simplify it. We can rewrite 90 as 9 * 10. Since the square root of 9 is 3, we can simplify √90 as 3√10. Since √10 cannot be simplified further, this number is not rational.
4. √125: To determine if √125 is rational, we can simplify it. The square root of 125 is 5√5. Since √5 cannot be simplified further, this number is not rational.
Therefore, the rational numbers in the given list are √81.