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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