**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:

√5

**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 √n , 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 2√5 + √3 ?(A) -2√5 + √3(B) -2√5 – √3(C) 2√3 – √5(D) √3 + 2√5Answer:**

(A) -2√5 + √3

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

(B) 68

Hints:

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

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

∴10 x = [/latex]0.\dot { 4 }[/latex]

∴10 – x = [/latex]4.\dot { 4 }[/latex] – [/latex]0.\dot { 4 }[/latex]

∴9x = 4

∴ x = 4/9

∴ Order = 6

ix. The conjugate of 2√5 + √3 is 2√5 – √3 or -2√5 + √3

x. |12 – (13+7) x 4| = |12 – 20 x 4|

= |12 – 80|

= |-68|

= 68

Solution:

∴ 999x = 29539

∴ 999x = 9306

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

Thus, multiplying both sides by 1000,

1000x = 357417.417417…

∴ 1000x = 357417.417 …(ii)

Subtracting (i) from (ii),

∴ 999x = 357060

∴ 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= 30219.219219…

∴ 999x = 30189

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

ii. 9/11

iii. √5

**Question 4.Show that 5 + √7 is an irrational number. [3 Marks]Solution:**

Let us assume that 5 + √7 is a rational number. So, we can find co-prime integers ‘a’ and ‘b’ (b ≠ 0) such that

Our assumption that 5 + √7 is a rational number is wrong.

∴ 5 + √7 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, 4√2 x √2 = 4 x 2 = 8, which is a rational number.

∴ √2 is the simplest form of the rationalising factor of √32 .

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

∴ √2 is the simplest form of the rationalising factor of √50 .

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

∴ √ 3 is the simplest form of the rationalising factor of √27 .

= 6, which is a rational number.

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

∴ √2 is the simplest form of the rationalising factor of 3√72.

vi. 4√11

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

∴ √11 is the simplest form of the rationalising factor of 4√11.

**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 π, 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.**