CHECK IF THE RADICAL IS RATIONAL OR IRRATIONAL WORKSHEET

Tell whether each expression is rational or irrational.

Problem 1 :

-√64

Solution

Problem 2 :

√1600

Solution

Problem 3 :

±√160

Solution

Problem 4 :

√144

Solution

Problem 5 :

√125

Solution

Problem 6 :

-√340

Solution

Problem 7 :

√1.96

Solution

Problem 8 :

-√0.09

Solution

Problem 9 :

Which statement is not always true?

1) The sum of two rational numbers is rational.

2) The product of two irrational numbers is rational.

3) The sum of a rational number and an irrational number is irrational.

4) The product of a nonzero rational number and an irrational number is irrational.

Solution

Problem 10 :

(-2 - √3) (-2 + √3) when simplifies is 

a) Positive and irrational       b) Positive and rational

c) Negative and irrational      d) negative and rational

Solution

Problem 11 :

Given that following expressions.

I  -5/8 + 3/5      II. 1/2 + √2      III. √5 √5     IV. 3√49

Which expression(s) result in an irrational number?

1) II, only      2) III, only      3) I, III, IV       4) II, III, IV

Solution

Problem 12 :

A teacher wrote the following set of numbers on the board:

a = √20, b = 2.5 and c = √225

explain why a + b is irrational, but b + c is rational

Solution

Classify each number as RATIONAL (Q) or IRRATIONAL (I)

Problem 1 :

√47

Solution

Problem 2 :

11/9

Solution

Problem 3 :

19/4

Solution

Problem 4 :

√96

Solution

Problem 5 :

19/14

Solution

Problem 6 :

15/4

Solution

Problem 7 :

√84

Solution

Problem 8 :

-9

Solution

Problem 9 :

√72

Solution

Problem 10 :

0

Solution

Problem 11 :

8/9

Solution

Problem 12 :

3

Solution

Problem 13 :

Determine if the product of 3√2 and 8 √18 is rational or irrational ? Explain your answer.

Solution

Problem 14 :

Which of the following numbers is irrational?

a) 0.252525…     b) 0.875       c) 0.3754152…     d) -0.121212… 

Solution

Problem 15 :

The product of any two irrational numbers is:

a) always an irrational number           b) always a rational number

c) always an integer             d) sometimes rational, sometimes irrational

Solution

Problem 16 :

Between two rational numbers:

a) there is no rational number          b) there is exactly one rational number

c) there are infinitely many rational numbers

d) there are only rational numbers and no irrational numbers

Solution

Problem 17 :

If a = -2 , b = -1, then find 𝑎^−𝑏 − 𝑏^𝑎.

Solution

Problem 18 :

Find the three rational numbers between:

(i) -1 and -2

(ii) 0.1 and 0.11

Solution

Problem 1 :

Which irrational numbers is between 4 and 5.

a. √12    b.√20    c. √34     d. √80

Solution

Problem 2 :

Which number is an integer ?

a. -11/5    b.-7    c. √15     d. 1/2

Solution

Problem 3 :

Which number is irrational ?

a. 9.2727....    b.√2    c. 5√9     d. -37/71

Solution

Problem 4 :

Which of the following is a rational number but is NOT an integer?

a. 8     b. 24      c. 40/4     d. 6.2

Solution

Problem 5 :

Barbara was asked to create a set of numbers that contained only integers. Which of the sets does NOT contain only integers?

a. {11, 6, -3, -4, 600, 24/12}

b. {9, 100, -4, 12, -6, 20/5}

c. {5, 3, -8, -14, 3.5, 24/12}

d. {22, -12.0, 9, -14, 28, 4}

Solution

Problem 6 :

Rational numbers are a dense set. This means that between any two rational numbers on a number line there is another rational number. Which rational number is between 2.46 and 2.47 on a number line?

a. 2.48   b. G 2.4   c. 2.53    d. 2.468

Solution

Problem 7 :

Which statement is NOT true about rational numbers?

a. The sum of two rational numbers is also a rational number.

b. 0 is not a rational number.

c. The product of two rational numbers is also a rational number.

d. The opposite of a rational number is also a rational number.

Solution

Problem 8 :

i) √40 has an infinite non repeating decimal expansion.

ii)  The number 0.5656...... is a rational number.

iii)  -200 and 500 are integers

iv)  All numbers with infinite decimal expansions are irrational.

v)  The numbers -8, -3, 5, 17 are all whole numbers.

Solution

Problem 9 :

Which number is irrational

a. 9.2727.....      b.√2         c. 5√9       d.-37/71

Solution

Problem 10 :

Any number with a finite decimal expansion must be 

a. rational    b. irrational

Solution

Problem 11 :

All integers are 

a.  Whole      b. rational    c. irrational

Solution

Problem 12 :

For what value of P and W is P + W a rational number ?

a.  P = 1/√3 and W = 1/√6               b. P = 1/√4 and W = 1/√9

c. P = 1/√6 and W = 1/√10               d. P = 1/√25 and W = 1/√2

Solution