Real Numbers | Class 9 | Problem Set 2

Real Numbers | Class 9 | Problem Set 2

Real Numbers | Class 9 | Problem Set 2, examples related to real numbers and surds are solved in this article.

Problem-Set-2

The pdf file embedded in this post contains solutions based on the following concepts –

(1) Proving the given number as an irrational number.

(2) Plotting an irrational number on the number line.

(3) Identifying whether the given number is surd or not.

(4) Simplification of the given surd.

(5) Addition and subtraction of the surds.

(6) Finding the simple rationalising factor of the surd.

(7) Rationalising the surd.

(8) Conversion of a given number to decimal form.

(9) Conversion of a number from decimal form to rational form.

(10) Determining the order of the surd.

(11) Finding the absolute value of a given expression.

(12) Deciding the nature of a decimal number.

(13) Finding the conjugate pair of a surd.

Also read : Sets | Class 9 | Practice Set 1.1

The questions answered in this article are listed below –

Class 9 | Problem Set 2 :

(1) Choose the correct alternative answer for the questions given below.
(i) Which one of the following is an irrational number ?
(A) 25 (B) 5 (C) 9 (D) 196

(ii) Which of the following is an irrational number?
(A) 0.17 (B) 1.513 (C) 0. 2746 (D) 0.101001000….

(iii) Decimal expansion of which of the following is non-terminating recurring ?

(iv) Every point on the number line represent, which of the following numbers?
(A) Natural numbers (B) Irrational numbers (C) Rational numbers (D) Real numbers

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.

(vii) Which of the following is not a surd ?

Also read : Sets | Class 9 | Practice Set 1.2

(viii) What is the order of the surd ?
(A) 3 (B) 2 (C) 6 (D) 5

(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 5

(x) The value of | 1/2 – (13+7) 4| is ……………
(A) -68 (B) 68 (C) -32 (D) 32.

(2) Write the following numbers in p/q form.
(i) 0.555 (ii) 29.568 (iii) 9.315 315 … (iv) 357.417417… (v)30. 219

(3) Write the following numbers in its decimal form.

(4) Show that 5 + 7 is an irrational number.

(5) Write the following surds in simplest form.

(6) Write the simplest form of rationalising factor for the given surds.

(7) Simplify.

(8) Rationalise the denominator.