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Operations on Rational and Irrational Numbers Answers

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1
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is

Question illustration
A
rational because it is a terminating decimal.
B
irrational because it is a repeating decimal.
C
irrational because it is a non-terminating and non-repeating decimal.
D
rational because it is a non-terminating and non-repeating decimal.
2
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How do you know that the sum of and is rational?

Question illustration
A
The sum is a terminating and a repeating decimal.
B
The sum is a non-terminating and a non-repeating decimal.
C
The sum is a fraction.
D
The sum is an integer.
3

Which of the following is irrational?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
4

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 square of rational numbers is irrational, and sum of two irrational numbers is irrational.
B
The product of two rational numbers is rational, and the sum of two rational numbers is irrational.
C
The left side of the equation will result in a rational number, which is a perfect square.
D
The left side of the equation will result in a rational number, which could be a non-perfect square.
5

Below is a proof showing that the sum of a rational number and an irrational number is an irrational number.Which of the following best completes the proof?

Question illustration
A
it is the sum of two rational numbers.
B
it is the sum of two irrational numbers.
C
it represents a non-terminating, non-repeating decimal.
D
its terms cannot be combined.
6

Which number is not a rational number?

A
mc006-1.jpg
Option A
B
mc006-2.jpg
Option B
C
7.608
D
mc006-3.jpg
Option D
7

Which statement is true about the sum of two rational numbers?

A
It can always be written as a fraction.
B
It can never be written as a fraction.
C
It can always be written as a repeating decimal.
D
It can never be written a terminating decimal.
8

Which number is irrational?

A
mc014-1.jpg
Option A
B
mc014-2.jpg
Option B
C
mc014-3.jpg
Option C
D
mc014-4.jpg
Option D
9

To find the area of a trapezoid, Dylan uses the formula The bases have lengths of 3.6 cm and cm. The height of the trapezoid is cm. The area of the trapezoid is irrational because

Question illustration
A
the values of the variables are all irrational numbers.
B
the entire answer is being multiplied by a fraction.
C
the height is irrational, and it is multiplied by the other rational dimensions.
D
the bases have an irrational sum that will be multiplied by the rational height.
10

Which of the following is rational?

A
mc009-1.jpg
Option A
B
mc009-2.jpg
Option B
C
mc009-3.jpg
Option C
D
mc009-4.jpg
Option D
11

The sum of two rational numbers will always be

A
an irrational number.
B
an integer.
C
a rational number.
D
a whole number.
12

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

A
rational.
B
irrational.
C
a repeating decimal.
D
a fraction.
13

The product of two rational numbers can always be written as

A
an irrational number.
B
a whole number.
C
an integer.
D
a fraction.
14

Which of the following will result in a rational answer?

A
multiplying by a fraction
Option A
B
adding the square root of a non perfect square to a whole number
C
adding the square root of a perfect square to
Option C
D
multiplying a fraction by a repeating decimal.
15

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 trapezoid
C
the formula for the area of a triangle
D
the formula for the area of a rectangle
16

mc011-1.jpg

Question illustration
A
5
B
mc011-2.jpg
Option B
C
6
D
mc011-3.jpg
Option D

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