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# 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) 