Write in descending order.
(i) 9/√2, 3/2 √5, 4√3, 3√(6/5)
(ii) 5/√3, 7/3 √2, -√3, 3√5, 2√7
Solution:
(i) 9/√2, 3/2 √5, 4√3, 3√(6/5)
9/√2 = (9×√2)/(√2×√2) = 9√2/2 = √((81/4)×2) = √(81/2) = √40.5
3/2 √5 = √((9/4)×5) = √(45/4) = √11.25
4√3 = √(16×3) = √48
3√(6/5) = √((9×6)/5) = √(54/5) = √10.8
Now, let us arrange in descending order
√48, √40.5, √11.25, √10.8
So,
4√3, 9/√2, 3/2 √5, 3√(6/5)
(ii) 5/√3, 7/3 √2, -√3, 3√5, 2√7
5/√3 = √(25/3) = √8.33
7/3 √2 = √((49/9) ×2) = √98/9 = √10.88
-√3 = -√3
3√5 = √(9×5) =√45
2√7 = √(4×7) = √28
Now, let us arrange in descending order
√45, √28, √10.88.., √8.33.., -√3
So,
3√5, 2√7, 7/3√2, 5/√3, -√3
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