Question

ALICIUL
1.
(v) 3+2.5
(i) 12
Prove that the following are irrational.
I
(ii) 13 + 15 (iii) 6 + 2 (iv) 15
Prove that p+Tg is an irrational, where p, q are primes.
2.​

Answer 1

Answer:

yo boom

Step-by-step explanation:

1. Insert a rational number between and 2/9 and 3/8 arrange in descending order.

Solution:

Given:

Rational numbers: 2/9 and 3/8

Let us rationalize the numbers,

By taking LCM for denominators 9 and 8 which is 72.

2/9 = (2×8)/(9×8) = 16/72

3/8 = (3×9)/(8×9) = 27/72

Since,

16/72 < 27/72

So, 2/9 < 3/8

The rational number between 2/9 and 3/8 is

ML Aggarwal Solutions for Class 9 Maths Chapter 1 – image 1

Hence, 3/8 > 43/144 > 2/9

The descending order of the numbers is 3/8, 43/144, 2/9

2. Insert two rational numbers between 1/3 and 1/4 and arrange in ascending order.

Solution:

Given:

The rational numbers 1/3 and ¼

By taking LCM and rationalizing, we get

ML Aggarwal Solutions for Class 9 Maths Chapter 1 – image 2

= 7/24

Now let us find the rational number between ¼ and 7/24

By taking LCM and rationalizing, we get

ML Aggarwal Solutions for Class 9 Maths Chapter 1 – image 3

= 13/48

So,

The two rational numbers between 1/3 and ¼ are

7/24 and 13/48

Hence, we know that, 1/3 > 7/24 > 13/48 > ¼

The ascending order is as follows: ¼, 13/48, 7/24, 1/3

Answer 2

Answer:

let us assume to a contrary that 3+2√5 is rational

now, let 3+2√5=a/b where a and b are coprime and b not equal to 0

now ,

2√5=a/b - 3

√5= 1/2(a/b-3)

we know that √5 is irrational

so that contradicts that our assumption is false

•°• 3+2√5 is irrational.