Answer :
i. 7√2 , 5√3
(7√2)2 = 7 × 7 × √2 × √2
⇒ (7√2)2 = 49 × 2
⇒ (7√2)2 = 98
And
(5√3)2 = 5 × 5 × √3 × √3
⇒ (5√3)2 = 25 × 3
⇒ (5√3)2 = 75
Clearly,
98 > 75
∴ 7√2 > 5√3
ii. √247, √274
(√247)2 = 247
And
(√274)2 = 274
Clearly,
247 < 274
∴ √247 < √274
iii. 2√7, √28
(2√7)2 = 2 × 2 × √7 × √7
⇒ (2√7)2 = 4 × 7
⇒ (2√7)2 = 28
And
(√28)2 = 28
Clearly,
28 = 28
∴ 2√7 = √28
iv. 5√5, 7√2
(5√5)2 = 5 × 5 × √5 × √5
⇒ (5√5)2 = 25 × 5
⇒ (5√5)2 = 125
And
(7√2)2 = 7 × 7 × √2 × √2
⇒ (7√2)2 = 49 × 2
⇒ (7√2)2 = 98
Clearly,
125 = 98
∴ 5√5= 7√2
v. 4√42, 9√2
(4√42)2 = 4 × 4 × √42 × √42
⇒ (4√42)2 = 16 × 42
⇒ (4√42)2 = 672
And
(9√2)2 = 9 × 9 × √2 × √2
⇒ (9√2)2 = 81 × 2
⇒ (9√2)2 = 162
Clearly,
672 > 162
∴ 4√42 > 9√2
vi. 5√3, 9
(5√3)2 = 5 × 5 × √3 × √3
⇒ (5√3)2 = 25 × 3
⇒ (5√3)2 = 75
And
(9)2 = 9 × 9
⇒ (9)2 = 81
Clearly,
75 < 81
∴ 5√3 < 9
vii. 7, 2√5
(2√5)2 = 2 × 2 × √5 × √5
⇒ (2√5)2 = 4 × 5
⇒ (2√5)2 = 20
And
(7)2 = 7 × 7
⇒ (7)2 = 49
Clearly,
49 > 20
∴ 7 > 2√5
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