# NUMBER SYSTEMS – Exercise 1.5 – (MATHEMATICS) – 9th Class

**Exercise 1.5**

**1. Classify the following numbers as rational or irrational :**

(i) 2-

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**Ans. –**2- is an irrational number, as difference of a rational and an irrational number is irrational.

(ii) (3 + ) –

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**Ans. –**, is a rational number.

(iii)

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**Ans. –**, is a rational number.

(iv)

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**Ans. –**is an irrational number, as divisors of an irrational number by a non-zero rational number is irrational.

(v) 2π

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**Ans. –**2π irrational number, as it is an irrational number and multiplication of a rational and an irrational number is irrational.

**2. Simplify each of the following expressions :**

(i) (3 + √5 ) (2 + √2)

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Ans. –

(ii) (3 + √3) (3 – √3)

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Ans. –

(iii) ( √5 + √2)²

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Ans. –

(iv) (√5 – √2) (√5 + √2)

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Ans. –

**3. Recall, π it is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, π = **

** This seems to contradict the fact that r is irrational. How will you resolve this contradiction?**

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**Sol.**On measuring c with any device, we get only approximate measurement. Therefore, π is an irrational.

**4. Represent on the number line.**

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**Sol.**

Let OA = 9.3 and OB = 1.

With AB as diameter draw a semicircle. Draw OP perpendicular to AB, meeting the semicircle at P. Then OP = . With O as centre and OP as radius draw an arc to meet the number line at Q on the positive side. Then, OQ = and the point Q thus obtained represents

.

**5. Rationalise the denominators of the following.**

(i)

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Ans. –

(ii)

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Ans. –

(iii)

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Ans. –

(iv)

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Ans. –