## RS Aggarwal Class 9 Ex 1A Chapter 1

**Question 1: What are irrational numbers? How do they differ from rational numbers? Give examples.**

**Solution: **

A number that can neither be expressed as a terminating decimal nor be expressed as a repeating decimal is called an irrational number. A rational number, on the other hand is always a terminating decimal, and if not, it is a repeating decimal.

Examples of irrational numbers:

0.101001000..

0.232332333..

**Question 2: Classify the following numbers as rational or irrational. Give reasons to support your SOLUTION. **

(i)

**(ii) 196−−−√**

**(iii) 21−−√ = 3–√ x 7–√**

**(iv) 43−−√**

**(v) 3 + 3–√**

**(vi) 7–√ – 2**

**(vii) 236–√**

**(viii) .66666666 **

**(ix) 1.232332333… **

**(x) 3.040040004… **

**(xi) 3.2576 **

**(xii) 2.356565656… **

**(xiii) π**

**(xiv) 227**

**Solution: **

(i)

It is a rational number.

(ii)

It is a rational number.

(iii)

It is an irrational number.

(iv)

If a is a positive integer, which is not a perfect square, then

Here, 43 is not a perfect square, so it is irrational.

(v) 3 +

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

So, it is an irrational number.

(vi)

The difference of an irrational number and a rational number is an irrational number, so it is an irrational number.

(vii)

The product of a rational number and an irrational number is an irrational number, so it is an irrational number.

(viii) .66666666

It is a rational number because it is a repeating decimal.

(ix) 1.232332333…

It is an irrational number because it is a non-terminating, non- repeating decimal.

(x) 3.040040004…

It is an irrational number because it is a non- terminating, non- repeating decimal.

(xi) 3.2576

It is a rational number because it is a terminating decimal.

(xii) 2.356565656…

It is a rational number because it is repeating.

(xiii)

It is an irrational number because it is a non – terminating, non – repeating decimal.

(xiv)

**Question 3: Represent 2–√ , 3–√ and 5–√ on the real line .**

**Solution: **

Let X’ OX be a horizontal line taken as the x – axis and O be the origin representing 0.

Take OA = 1 unit and AB

Join OB

Now,

OB =

Taking O as the center and OB as the radius, draw an arc, meeting OX at P

We have:

OP = OB =

Thus, point P represents

Now, draw BC

Join OC

We have:

OC =

Taking O as the centre and OC as the radius, draw an arc, meeting OX at Q.

We have:

OQ = OC =

Thus, point Q represents

Now, draw CD

Join OD

We have:

OD =

Now, draw DE

Join OE.

We have:

Taking O as the center and OE as the radius, draw an arc, meeting OX at R.

We have:

OR = OE =

Thus, point R represents

**Question 4: Represent 6–√ , 7–√ and 5–√ on the real line .**

**Solution: **

Let X’OX be a horizontal line taken as the x – axis and O be the origin representing 0.

Take OA = 2 units and AB

Now join OB.

We have: OB =

Taking O as the center and OB as the radius, draw an arc, meeting OX at P .

Thus, we have:

OP = OB =

Here, point P represents

Now, draw BC

Join OC

We have: OC =

Taking O as the centre and OC as the radius, draw an arc, meeting OX at Q.

Thus, we have:

OQ = OC =

Here, point Q represents

Now, draw CD

Join OD.

We have: OD =

Taking O as the centre and OE as the radius, draw an arc, meeting OX at R.

Now,

OR = OD =

Thus, point R represents

**Question 5: Giving reason in each case, show that each of the following members is irrational.**

**4 +**5–√ **– 3 +**6–√ 57–√ −38–√ 25√ 43√

**Solution: **

(i) 4 +

(ii) – 3 +

(iii)

(iv)

(v)

(vi)

**Question 6: State in each case, whether the given statement is true or false.**

**The sum of two rational number is rational.****The sum of two irrational number is irrational.****The product of two rational number is rational.****The product of two irrational numbers is irrational.****The sum of a rational number and irrational number is irrational.****The product of rational number and irrational number is a rational number.****Every real number is rational.****Every real number is rational or irrational.**π is irrational and227 is rational.

**Solution: **

(i) True

(ii) False

Example: ( 2 +

Here, 4 is a rational number.

(iii) True

(iv) False

Example:

Here, 3 is a rational number.

(v) True

(vi) False

Example: (4) x

Here,

(vii) False

Real numbers can be divided into rational and irrational numbers.

(viii) True

(ix) True

**Question 7: ADD;**

**(i) 2 3–√ – 52–√ and 3–√ + 22–√**

**(ii) 2 2–√ + 53–√ – 75–√ and 33–√ – 2–√ + 5–√**

**(iii) 237–√ – 122–√ +611−−√ and 137–√ + 322–√ – 11−−√**

**Solution: **

(i) 2

= (2

= 3

(ii) 2

= 2

=

(iii)

=

=

**Question 8: MULTIPLY;**

**3**5–√ by 25–√ **6**15−−√ by 43–√ **2**6–√ by 33–√ **3**8–√ by 32–√ 10−−√ by40−−√ **3**28−−√ by 27–√

**Solution:**

(i) 3

(ii) 6

(iii) 2

(iv) 3

(v)

(vi) 3

**Question 9: DIVIDE ;**

166–√,by42–√ 166–√,by42–√ 166–√,by42–√

**Solution: **

(i)

(ii)

(iii)