Q. Which is the greatest among √(6) + √(4) , √(8) + √(3) , √(12) + √(2) and √(24) + √(1) ?
Option: A)√(6) + √(4) B) √(8) + √(3) C) √(12) + √(2) d) √(24) + √1
Soln
Multiply the numbers inside each root: i. 6 × 4 = 24, ii. 8 × 3 = 24, iii. 12 × 2 = 24, iv. 24 × 1 = 24
Product is same in all options.
Now compare the first numbers: 6 , 8 , 12 , 24 ← biggest
So, the greatest is (D) √24 + √1.
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Practice Set
Q1. Which is greatest ?
A) √2 + √8 B) √4 + √4 C) √1 + √16 D) √3 + √(16/3)
Q2. Which is greatest ?
A) √5 + √20 B) √10 + √10 C) √2 + √50 D) √1 + √100
Q3. Which is greatest ?
A) √6 + √24 B) √8 + √18 C) √12 + √12 D) √2 + √72
Q4. Which is greatest ?
A) √7 + √28 B) √14 + √14 C) √4 + √49 D) √1 + √196
Q5. Which is greatest ?
A) √15 + √60 B) √20 + √45 C) √12 + √75 D) √1 + √900
Q6. Which is greatest ?
A) √18 + √72 B) √24 + √54 C) √36 + √36 D) √2 + √648
Trick: If (inside 1st root) × (inside 2nd root) is same in all options: The option with the largest first number is greatest.