**Chapter 2 Real Numbers Practice Set 2**

Chapter 2 Real Numbers Practice Set 2

**Question 1.Choose the correct alternative answer for the questions given below. [1 Mark each]**

**i. Which one of the following is an irrational number?**

Answer:

Answer:

âˆš5

**ii. Which of the following is an irrational number?**

**iii. Decimal expansion of which of the following is non-terminating recurring?Answer:**

(C) 3/11

iv. Every point on the number line represents which of the following numbers?

(A) Natural numbers

(B) Irrational numbers

(C) Rational numbers

(D) Real numbers

Answer:

(D) Real numbers

Answer:

(A) 4/9

**vi. What is âˆšn , if n is not a perfect square number ?(A) Natural number(B) Rational number(C) Irrational number(D) Options A, B, C all are correct.Answer:**

(C) Irrational number

**vii. Which of the following is not a surd ?Answer:**

(A) 3

(B) 2

(C) 6

(D) 5

Answer:

(C) 6

**ix. Which one is the conjugate pair of 2âˆš5 + âˆš3 ?(A) -2âˆš5 + âˆš3(B) -2âˆš5 â€“ âˆš3(C) 2âˆš3 â€“ âˆš5(D) âˆš3 + 2âˆš5Answer:**

(A) -2âˆš5 + âˆš3

**x. The value of |12 â€“ (13 + 7) x 4| is ____ .(A) â€“ 68(B) 68(C) â€“ 32(D) 32Answer:**

(B) 68

Hints:

ii. Since the decimal expansion is neither terminating nor recurring, 0.101001000â€¦. is an irrational number.

v. Let x = [/latex]0.\dot { 4 }[/latex]

âˆ´10 x = [/latex]0.\dot { 4 }[/latex]

âˆ´10 â€“ x = [/latex]4.\dot { 4 }[/latex] â€“ [/latex]0.\dot { 4 }[/latex]

âˆ´9x = 4

âˆ´ x = 4/9

âˆ´ Order = 6

ix. The conjugate of 2âˆš5 + âˆš3 is 2âˆš5 â€“ âˆš3 or -2âˆš5 + âˆš3

x. |12 â€“ (13+7) x 4| = |12 â€“ 20 x 4|

= |12 â€“ 80|

= |-68|

= 68

Solution:

âˆ´ 999x = 29539

âˆ´ 999x = 9306

Since, three numbers i.e. 4, 1 and 7 are repeating after the decimal point.

Thus, multiplying both sides by 1000,

1000x = 357417.417417â€¦

âˆ´ 1000x = 357417.417 â€¦(ii)

Subtracting (i) from (ii),

âˆ´ 999x = 357060

âˆ´ x = 30.219219

Since, three numbers i.e. 2, 1 and 9 are repeating after the decimal point.

Thus, multiplying both sides by 1000,

1000x= 30219.219219â€¦

âˆ´ 999x = 30189

**Question 3.Write the following numbers in its decimal form.Solution:**

ii. 9/11

iii. âˆš5

**Question 4.Show that 5 + âˆš7 is an irrational number. [3 Marks]Solution:**

Let us assume that 5 + âˆš7 is a rational number. So, we can find co-prime integers â€˜aâ€™ and â€˜bâ€™ (b â‰ 0) such that

Our assumption that 5 + âˆš7 is a rational number is wrong.

âˆ´ 5 + âˆš7 is an irrational number.

**Question 5.Write the following surds in simplest form.Solution:**

**Question 6.Write the simplest form of rationalising factor for the given surds.Solution:**

Now, 4âˆš2 x âˆš2 = 4 x 2 = 8, which is a rational number.

âˆ´ âˆš2 is the simplest form of the rationalising factor of âˆš32 .

Now, 5âˆš2 x âˆš2 = 5 x 2 = 10, which is a rational number.

âˆ´ âˆš2 is the simplest form of the rationalising factor of âˆš50 .

Now, 3âˆš3 x âˆš3 = 3 x 3 = 9, which is a rational number.

âˆ´ âˆš 3 is the simplest form of the rationalising factor of âˆš27 .

= 6, which is a rational number.

Now, 18âˆš2 x âˆš2 = 18 x 2 = 36, which is a rational number.

âˆ´ âˆš2 is the simplest form of the rationalising factor of 3âˆš72.

vi. 4âˆš11

4âˆš11 x âˆš11 = 4 x 11 = 44, which is a rational number.

âˆ´ âˆš11 is the simplest form of the rationalising factor of 4âˆš11.

**Question 7.Simplify.Solution:**

**Question 8.Rationalize the denominator.Solution:**

**Question 1.Draw three or four circles of different radii on a card board. Cut these circles. Take a thread and measure the length of circumference and diameter of each of the circles. Note down the readings in the given table. (Textbook pg.no.23 )Solution:**

i. 14,44,3.1

ii. 16,50.3,3.1

iii. 11,34.6,3.1

**Question 2.To find the approximate value of Ï€, take the wire of length 11 cm, 22 cm and 33 cm each. Make a circle from the wire. Measure the diameter and complete the following table.**