Mathematics Part i Solutions Solutions for Class 9 Maths Chapter 2 Real Numbers are provided here with simple step-by-step explanations. These solutions for Real Numbers are extremely popular among class 9 students for Maths Real Numbers Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Mathematics Part i Solutions Book of class 9 Maths Chapter 2 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Mathematics Part i Solutions Solutions. All Mathematics Part i Solutions Solutions for class 9 Maths are prepared by experts and are 100% accurate.
Page No 21:
Question 1:
Classify the decimal form of the given rational numbers into terminating and non-terminating recurring type.
Answer:
Since,
The denominator is in the form of , where m and n are non-negative integers.
So, the decimal form of will be terminating type.
Since,
The denominator is not in the form of , where m and n are non-negative integers.
So, the decimal form of will be non-terminating recurring type.
Since,
The denominator is in the form of , where m and n are non-negative integers.
So, the decimal form of will be terminating type.
Since,
The denominator is in the form of , where m and n are non-negative integers.
So, the decimal form of will be terminating type.
Since,
The denominator is not in the form of , where m and n are non-negative integers.
So, the decimal form of will be non-terminating recurring type.
Page No 21:
Question 2:
Write the following rational numbers in decimal form.
Answer:
â
â
â
â
Page No 21:
Question 3:
Write the following rational numbers in form
Answer:
â
â
â
â
Page No 25:
Question 1:
Show that 4 is an irrational number.
Answer:
Let us assume that 4 is a rational number.
4 = , where p and q are the integers and q 0.
=
Since, p, q and 4 are integers. So, is a rational number.
is also a rational number.
but this contradicts the fact that is an irrational number.
This contradiction has arisen due to the wrong assumption that 4 is a rational number.
Hence, 4 is an irrational number.
Page No 25:
Question 2:
Prove that 3 + is an irrational number.
Answer:
Let us assume that 3 + is a rational number.
3 + = , where p and q are the integers and q 0.
=
Since, p, q and 3 are integers. So, is a rational number.
is also a rational number.
but this contradicts the fact that is an irrational number.
This contradiction has arisen due to the wrong assumption that 3 + is a rational number.
Hence, 3 + â is an irrational number.
Page No 25:
Question 3:
Represent the numbers and on a number line .
Answer:
(i) Steps of construction for :
Step 1: Draw a number line. Mark O as the zero on the number line.
Step 2: At point A, draw AB OA such that AB = 1 unit.
Step 3: With point O as the centre and radius OB, draw an arc intersecting the number line at point P.
Thus, P is the point for on the number line.
(ii) Steps of construction for :
Step 1: Draw a number line. Mark O as the zero on the number line.
Step 2: At point A, draw AB OA such that AB = 1 unit.
Step 3: With point O as the centre and radius OB, draw an arc intersecting the number line at point C.
Thus, C is the point for â on the number line.
Page No 25:
Question 4:
(i) 0.3 and -0.5
Answer:
(iv) The three rational numbers between 4.5 and 4.6 are 4.51, 4.55, and 4.59
Page No 30:
Question 1:
State the order of the surds given below.
Answer:
The order of the surd is 3.
The order of the surd is 2.
The order of the surd is 4.
The order of the surd is 2.
The order of the surd is 3.
Page No 30:
Question 2:
State which of the following are surds. Justify.
(i) (ii) (iii) (iv) (v) (vi)
Answer:
(i) Since,
So, is a surd.
(ii) Since,
So, is not a surd.
(iii) Since,
So, is a surd.
(iv) Since,
So, is not a surd.
(v) Since,
So, is not a surd.
(vi) Since,
So, is a surd.
Page No 30:
Question 3:
Classify the given pair of surds into like surds and unlike surds.
(i) (ii) (iii) (iv) (v) (vi)
Answer:
(i)
Since,
So, is like surds.
(ii)
Since,
So, is unlike surds.
(iii)
Since,
So, is like surds.
(iv)
Since,
So, is like surds.
(v)
Since,
So, is unlike surds.
(vi)
Since,
So, is like surds.
Page No 30:
Question 4:
Simplify the following surds.
(i) (ii) (iii) (iv) (v)
Answer:
(i)
(ii)
(iii)
(iv)
(v)
Page No 30:
Question 5:
Compare the following pair of surds.
(i) (ii) (iii) (iv) (v) (vi) (vii)
Answer:
(i)
Since,
So,
(ii)
(iii)
Since,
So,
(iv)
Since,
So,
(v)
Since,
So,
(vi)
Since,
So,
(vii)
Since,
So,
Page No 30:
Question 6:
Simplify.
(i) (ii) (iii) (iv)
Answer:
(i)
(ii)
(iii)
(iv)
Page No 30:
Question 7:
Multiply and write the answer in the simplest form.
(i) (ii)
(iii) (iv)
Answer:
(i)
(ii)
(iii)
(iv)
Page No 30:
Question 8:
Divide, and write the answer in simplest form.
(i) (ii) (iii) (iv)
Answer:
(i)
(ii)
(iii)
(iv)
Page No 30:
Question 9:
Rationalize the denominator.
(i) (ii) (iii) (iv) (v)
Answer:
(i)
(ii)
(iii)
(iv)
(v)
Page No 32:
Question 1:
Multiply
(i) (ii) (iii)
Answer:
(i)
(ii)
(iii)
Page No 32:
Question 2:
Rationalize the denominator.
(i) (ii) (iii) (iv)
Answer:
(i)
(ii)
(iii)
(iv)
Page No 33:
Question 1:
Find the value.
(i) (ii) (iii)
Answer:
(i)
(ii)
(iii)
Page No 33:
Question 2:
Solve.
(i) (ii) (iii) (iv)
Answer:
(i)
(ii)
(iii)
(iv)
Page No 34:
Question 1:
(A) (B) (C) (D)
(iii) Decimal expansion of which of the following is non-terminating recurring ?
(A) (B) (C) (D)
(v) The number in form is .....
(A) (B) (C) (D)
(vi) What is , 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 ?
(A) (B) (C) (D)
(viii) What is the order of the surd ?
(A) 3 (B) 2 (C) 6 (D) 5
(ix) Which one is the conjugate pair of ?
(A) (B) (C) (D)
(x) The value of is...............
(A) 68 (B) 68 (C) 32 (D) 32
Answer:
= is a rational number; is a rational number; = 14 is a rational number; and is an irrational number.
Hence, the correct option is (B).
has non-terminating recurring decimal expansion, so, it is rational number;
has non-terminating recurring decimal expansion, so, it is rational number;
0.101001000..... has non-terminating non-recurring decimal expansion, so, it is irrational number;
Hence, the correct option is (D).
(iii)
(A) Since, 5 = , which is in the form of , where m and n are non-negative integers.
So, the decimal expansion of is terminating.
(B) Since, 16 = , which is in the form of , where m and n are non-negative integers.
So, the decimal expansion of is terminating.
(C) Since, 11 = , which is not in the form of , where m and n are non-negative integers.
So, the decimal expansion of â is non-terminating recurring.
(D) Since, 25 = , which is in the form of , where m and n are non-negative integers.
So, the decimal expansion of is terminating.
Hence, the correct option is (C).
Hence, the correct option is (D).
(v)
Hence, the correct option is (A).
(vi) If n is not a perfect square number, then is an irrational number.
Hence, the correct option is (C).
(vii) Since, = 4
Hence, the correct option is (C).
(viii) Since,
So, the order of the surd is 6.
Hence, the correct option is (C).
(ix) Since, the conjugate pair of () is ().
âHence, the correct option is (A).
(x) Since,
So, the value of is 68 .
âHence, the correct option is (B).
Page No 35:
Question 2:
Write the following numbers in form
(i ) 0.555 (ii) (iii) 9.315 315 ... (iv) 357.417417...
(v)
Answer:
(i ) 0.555
(ii)
(iii) 9.315 315 ...
(iv) 357.417417...
(v)
Page No 35:
Question 3:
Write the following numbers in its decimal form. .
(i) (ii) (iii) (iv) (v)
Answer:
(i)
(ii)
(iii)
(iv)
(v)
Page No 35:
Question 4:
Show that 5 + is an irrational number.
Answer:
Let us assume that 5 + is a rational number.
Since, .
is also a rational number.
But this contradicts the fact that is an irrational number.
This contradiction has arisen due to our assumption that 5 + is a rational number.
Hence, 5 + is an irrational number.
Page No 35:
Question 5:
Write the following surds in simplest form.
(i) (ii)
Answer:
(i)
(ii)
Page No 35:
Question 6:
Write the simplest form of rationalising factor for the given surds.
(i)
Answer:
Page No 35:
Question 7:
Simplify.
(i)
(ii)
(iii)
(iv)
(v)
Answer:
(i)
(ii)
(iii)
(iv)
(v)
Page No 35:
Question 8:
Rationalize the denominator.
(i) (ii) (iii) (iv) (v)
Answer:
(i)
(ii)
(iii)
(iv)
(v)
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