Compare the follo

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