AnswersAlgebra IOperations on Rational and Irrational Numbers

Operations on Rational and Irrational Numbers — Quiz Answers

10 verified answers
1
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Which of the following best completes the proof?

A
it is the sum of two irrational numbers
B
it represents a non-terminating, non-repeating decimal
C
its terms cannot be combined
D
it is the sum of two rational numbers
2
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To find the area of a trapezoid, Dylan uses the formula A=12⁢(b1+b2)⁢h. The bases have lengths of 3.6 cm and 1213 cm. The height of the trapezoid is 5 cm. The area of the trapezoid is irrational because

A
the bases have an irrational sum that will be multiplied by the rational height.
B
the values of the variables are all irrational numbers.
C
the entire answer is being multiplied by a fraction.
D
the height is irrational, and it is multiplied by the other rational dimensions.
3

Which of the following will result in a rational answer?

A
adding the square root of a perfect square to pi
B
adding the square root of a non perfect square to a whole number
C
multiplying pi by a fraction
D
multiplying a fraction by a repeating decimal
4

The product of two rational numbers can always be written as

A
a fraction.
B
an integer.
C
an irrational number.
D
a whole number.
5

Which number is not a rational number?

A
7 point 6 0 8
B
negative 5 and 4 over 11
C
18 point 4 repeating 6
D
square root of 31
6

How do you know that the sum of open paren negative 2 and 3 fourths close paren and 5 ninths is rational?

A
The sum is a non-terminating and a non-repeating decimal.
B
The sum is a fraction.
C
The sum is an integer.
D
The sum is a terminating and a repeating decimal.
7

The Pythagorean theorem states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse by the formula a2+b2=c2. If A is a rational number and b is a rational number, why could c be an irrational number?

A
The left side of the equation will result in a rational number, which could be a non-perfect square.
B
The product of two rational numbers is rational, and the sum of two rational numbers is irrational.
C
The square of rational numbers is irrational, and sum of two irrational numbers is irrational.
D
The left side of the equation will result in a rational number, which is a perfect square.
8

Why is the product of a rational number and an irrational number irrational?

A
because the product is always a non-terminating, non-repeating decimal
B
because the product is always a repeating or a terminating decimal
C
because the product is always a fraction
D
because the product is always a negative number
9

The sum or product of a non-zero rational number and an irrational number is always

A
rational.
B
irrational.
C
a fraction.
D
a repeating decimal.
10

Which of the following formulas, when evaluated using rational values for the variables, will result in an irrational number?

A
the formula for the area of a circle
B
the formula for the area of a triangle
C
the formula for the area of a rectangle
D
the formula for the area of a trapezoid

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