Chapter 3: Rationalisation Exercise – 3.1

Question: 1

Simplify each of the following:

Solution:

= (4³)^1/3

= 4^{(3 × 1/3)}

= 4¹

= 4

= 15^(4×1/4)

= 15

 

Question: 2

Simplify the following expressions:

Solution:

 

Question: 3

Simplify the following expressions:

Solution:

As we know, (a + b) (a - b) = (a² − b²)

So, 11² - 11

121 - 11 = 110

As we know, (a + b) (a - b) = (a² − b²)

So, 5² - 7

25 - 7 = 18

As we know, (a + b) (a - b) = (a² − b²)

= 6

As we know, (a + b) (a - b) = (a² − b²)

= 6

As we know, (a + b) (a - b) = (a² − b²)

= 5 - 2

= 3

 

Question: 4

Simplify the following expressions:

Solution:

As we know, (a + b)² = (a² + 2 × a × b + b²)

As we know, (a - b)²  = (a² − 2 × a × b + b²)

As we know, (a + b)² = (a² + 2 × a × b + b²)