Q. 54.1( 31 Votes )

# Compare the follo

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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