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AP Board Class 9 Maths Chapter 1 Real Numbers Ex 1.4 Textbook Solutions PDF: Download Andhra Pradesh Board STD 9th Maths Chapter 1 Real Numbers Ex 1.4 Book Answers

 AP Board Class 9 Maths Chapter 1 Real Numbers Ex 1.4 Textbook Solutions PDF: Download Andhra Pradesh Board STD 9th Maths Chapter 1 Real Numbers Ex 1.4 Book Answers

Andhra Pradesh State Board Class 9th Maths Chapter 1 Real Numbers Ex 1.4 Books Solutions

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AP Board Class 9th Maths Chapter 1 Real Numbers Ex 1.4 Textbooks Solutions with Answer PDF Download

Find below the list of all AP Board Class 9th Maths Chapter 1 Real Numbers Ex 1.4 Textbook Solutions for PDF’s for you to download and prepare for the upcoming exams:

AP State Syllabus 9th Class Maths Solutions 1st Lesson Real Numbers Exercise 1.4

Question 1.
Simple the following expressions.
i) (5 + √7) (2 + √5)
Solution:
(5 + √7) (2 + √5)
= 10 + 5√5 + 2√7 + √35

ii) (5 + √5) (5 – √5)
Solution:
(5 + √5) (5 – √5)
= 52 + (√5)2
= 25 – 5 = 20

(iii) (√3 + √7)2
Solution:
(√3 + √7)2
= (√3)2 + (√7)2 + 2(√3)(√7)
= 3 + 7 + 2√21
= 10 + 2√21

iv) (√11 – √7) (√11 + √7)
= (√11)2 – (√7)2
= 11 – 7 = 4

Question 2.
Classify the following numbers as rational or irrational.
i) 5 – √3
ii) √3 + √2
iii) (√2 – 2)2
iv) 27√77√
v) 2π
vii) (2 +√2) (2 – √2)
Solution:
i) 5 – √3 – irrational
ii) √3 + √2 – irrational
iii) (√2 – 2)2 – irrational
iv) 27√77√ – rational
v) 2π – Transcendental number. (not irrational)
vi) 13√– irrational
vii) (2 +√2) (2 – √2) – rational

Question 3.
In the following equations, find whether variables x, y, z etc., represents rational or irrational numbers.
i) x2 = 7
ii) y2 = 16
iii) z2 = 0.02
iv) u2 = 174
v) w2 = 27
vi) t4 = 256
Solution:
i) x2 = 7
⇒ x = √7 is an irrational number.
ii) y2 = 16 ⇒ y = 4 is a rational number.
iii) z2 = 0.02 ⇒ z = 0.02‾‾‾‾√ is an irrational number.
iv) u2 = 174 ⇒ x = 17√2 is an irrational number.
v) w2 = 27 ⇒ w = 33‾√ an irrational number.
vi) t4 = 256 ⇒ t2 = 256‾‾‾‾√ = 16
⇒ t = 16‾‾‾√ = 4 is a rational number

Qeustion 4.
The ratio of circumference to the diameter of a circle c/d is represented by π. But we say that π is an irrational number. Why?

Question 5.
Rationalise the denominators of the following.
i) 13+2√
Solution:

ii) 17√−6√
Solution:

iii) 17√
Solution:

iv) 6√3√−2√
Solution:

Question 6.
Simplify each of the following by rationalising the denominator.
i) 6−42√6+42√
Solution:

ii) 7√−5√7√+5√
Solution:

iii) 132√−23√
Solution:

iv) 35√−7√33√+2√
Solution:

Question 7.
Find the value of 10√−5√22√ upto three decimal places. (take 2‾√ = 1.414, 3‾√ = 1.732 and 5‾√ = 2.236).
Solution:

Question 8.
Find
i) 641/6
Solution:
= (26)1/6
= 6

ii) 321/5
Solution:
321/5
= (25)1/5
= 2

iii) 6251/4
6251/5
= (54)1/4
= 5

iv) 163/2
Solution:
163/2
= (42)3/2

v) 2432/5
Solution:
2432/5
= (35)2/5

vi) (46656)-1/6
Solution:

Question 9.
Simplify 81‾‾‾√4−8343‾‾‾‾√3+1532‾‾‾√5+225‾‾‾‾√
Solution:

Question 10.
If ‘a’ and ‘b’ are rational numbers, find the values of a and b in each of the following equations.
i) 3√+2√3√−2√=𝐚+𝐛6‾√
Solution:
Given that 3√+2√3√−2√=𝐚+𝐛6‾√
Rationalising the denominator we get

Comparing 5 + 2√6 with a + b√6
We have a = 5 and b = 2

ii) 5√+3√25√−33√=𝑎−𝑏15‾‾‾√
Solution:
Given that 5√+3√25√−33√=𝑎−𝑏15‾‾‾√
Rationalising the denominator we get

Andhra Pradesh Board Class 9th Maths Chapter 1 Real Numbers Ex 1.4 Textbooks for Exam Preparations

Andhra Pradesh Board Class 9th Maths Chapter 1 Real Numbers Ex 1.4 Textbook Solutions can be of great help in your Andhra Pradesh Board Class 9th Maths Chapter 1 Real Numbers Ex 1.4 exam preparation. The AP Board STD 9th Maths Chapter 1 Real Numbers Ex 1.4 Textbooks study material, used with the English medium textbooks, can help you complete the entire Class 9th Maths Chapter 1 Real Numbers Ex 1.4 Books State Board syllabus with maximum efficiency.

FAQs Regarding Andhra Pradesh Board Class 9th Maths Chapter 1 Real Numbers Ex 1.4 Textbook Solutions

Can we get a Andhra Pradesh State Board Book PDF for all Classes?

Yes you can get Andhra Pradesh Board Text Book PDF for all classes using the links provided in the above article.

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