Class 9 Maths - Number System Previous Year Questions

Sol:

√45 – 3√20 + 4√5

= 3√5 – 6√5 + 4√5

= √5.

Sol:

Sol:

Sol:

 Let x = 0.1, y = 0.3 and n = 2

∴ Two rational numbers between 0.1 and 0.3 are: x + d and x + 2d

Sol:

We have, Now, dividing 25 by 8,

Since, the remainder is 0.
∴ The process of division terminates.

Sol:

Since RF of (√x - √y ) is (√x +√y )
∴ RF of (√3 - √2 ) is (√3 +√2 )
Now, we have

Thus,  

Sol:

As per the question, We need to find drational numbers lying between 1/5 and 1/2 As we know,

• Rational Numbers are numbers that can be expressed in the form of p/q where q is not equal to zero.
• Now, we know that  1/5 = 0.2 and 1/2 = 0.5
• So, numbers between 0.2 and 0.5 are infinite. Some of them are 0.3,0.4,0.45,,0.35 etc.
• And these may be written as 3/10,4/10,45/100,35/100 tec.

Hence, Rational numbers between 1/2 and 1/5 are infinite. Some of them are 3/10 , 4/10 , 45/100 , 35/100. 

Sol:

Let X =  = 0.24545     ... (1)Then, multiplying (1) by 10,We have 10X = 10 x 0.24545...
⇒ 10x = 2.4545                      ... (2)
Again multiplying (1) by 1000,
we get 1000 x X = 0.24545... x 1000
⇒ 1000X = 245.4545                ... (3)
Subtracting (2) from (3),
1000X – 10X = 245.4545... – 2.4545...

Thus  

Sol:

We have x = 2 + √5
∴

∴ Now  

Sol: 

Let x = 1 and y = 2
⇒   y > x
Here n = 6

 ∴ The six rational numbers between 1 and 2 are: (x + d), (x + 2d), (x + 3d), (x + 4d), (x + 5d) and (x + 6d).

Sol:

Let x = 0.6 and y = 0.8
⇒   y > x
Here, n = 5
∴  Now, the five rational numbers between 0.6 and 0.8 are: (x + d), (x + 2d), (x + 3d), (x + 4d), and (x + 5d).

Thus, the required five rational numbers between 0.6 and 0.8 are: