Irrational Numbers and Properties of Irrational Numbers

Q. Prove that root 3 is an irrational number

Q.

Every rational number is a real number. Justify your answer

Q.

Can u give an example to show that the product of a rational number and an irrational number may be a rational number?

Q.

The product or quotient of a non-zero rational number with an irrational number is:

1. Natural number

2. Whole number

3. Rational number

4. Irrational number

Q.

Find the decimal expansion of 2\15

Q.

Irrational number between 1.011243... and 1.012243... is

1. 1.01152243 ...

2. 1.013243 ...

3. 1.012343 ...

4. 1.011143...

Q. Prove that root 2 is an irrational number

Q.

The simplest rationalization factor of √50 is:

1. √2

2. √50

3. 50

Q.

Why √2/1 is not a rational number? Where p = √2 and q=1 which is satisfying the need for a rational number.

Q.

Look at several examples of rational numbers in the form (q ≠ 0), where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions). Can you guess what property q must satisfy?

Q.

A number is irrational if and only if its decimal representation is:

1. Non- terminating and non-repeating

2. Non- terminating

3. Terminating

4. Non- terminating and repeating

Q.

π is a real number. State whether true or false.

1. True

2. False

Q. Question 3
Decimal representation of a rational number cannot be

A) Terminating
B) Non-terminating
C) Non-terminating repeating
D) Non-terminating non-repeating

Q.

Write the following in decimal form and say what kind of decimal expansion each has:

(i) (ii) (iii)

(iv) (v) (vi)

Q. What is pie ?
Is pie rational or irrational ?
Why ?

Q.

What can be the maximum number of entries in the repeating string of remainders in the decimal expansion of 3/7? Perform the division and write the repeating string of remainders

Q.

You know that. Can you predict what the decimal expansion of are, without actually doing the long division? If so, how?

[Hint: Study the remainders while finding the value of carefully.]

Q.

Is $\sqrt{2}$ a rational number?

Q. Which of the following is a true statment?
(a) $\mathrm{\pi }\mathrm{and}\frac{22}{7}$are both rationals
(b) $\mathrm{\pi }\mathrm{and}\frac{22}{7}$are both irrationals
(c) $\mathrm{\pi }$ is rational and $\frac{22}{7}$is irrational
(d) $\mathrm{\pi }$ is irrational and $\frac{22}{7}$is rational

Q. Prove that $\sqrt{5}$ is an irrational number.

Q. Prove that root 3 add root 3 is an irrational number.

Q.

The decimal expansions that correspond to rational numbers is.

1. Either terminating or recurring

2. Both terminating and recurring

3. Terminating

4. Recurring

Q.

What can the maximum number of digits be in the repeating block of digits in the decimal expansion of? Perform the division to check your answer.

Q. Decimal expansion of $\sqrt{2}$is
(a) a finite decimal
(b) a terminating or repeating decimal
(c) a non-terminating and non-repeating decimal
(d) none of these

Q.

Write three numbers whose decimal expansions are non-terminating, non-recurring.

Q.

Number having non terminating and repeating decimal expansion

Q. Which of the following is an irrational number?

(a) $\sqrt{\frac{9}{27}}$

(b) −$\sqrt{64}$

(c) $\sqrt{1.44}$

(d) $\sqrt{\frac{1}{4}}$

Q. Classify the following numbers as rational or irrational. Give reasons to support your answer:
(i) $\sqrt{4}$
(ii) $\sqrt{196}$
(iii) $\sqrt{21}$
(iv) $\sqrt{43}$
(v) $3+\sqrt{3}$
(vi) $\sqrt{7}-2$
(vii) $\frac{2}{3}\sqrt{6}$
(viii) $0.\overline{6}$
(ix) 1.232332333...
(x) 3.040040004....
(xi) 3.2576
(xii) 2.356565656...
(xiii) $\mathrm{\pi }$
(xiv) $\frac{22}{7}$

Q. Prove that 3 + $\sqrt{5}$ is an irrational number.

Q.

Show that 1.27 is rational number