Operations on Real NumbersPractice Questions & MCQs

Q1. Evaluate √(7 + √48) + √(7 - √48).

• A.4
• B.2
• C.7
• D.5

Answer: A. 4

Given 8730, 7, 8730, 48, 8730, asked for Evaluate √(7 + √48) + √(7 - √48). By sum of roots = 2×.2 = 4. √.48 = 4√.3 → 7±.4√.3 = (2±.√.3)^2 → sum of roots = 2×.2 = 4. Therefore option A) 4. Others fail: option B) '2' fails since √48 = 4√3; denest each term; option C) '7' is incorrect: Each root is 2±√3.

Q2. Evaluate √(11 + √72) + √(11 - √72).

• A.6
• B.3
• C.11
• D.7

Answer: A. 6

Diagnose the question type - a typical math numerical. The data on the table: 8730, 11, 8730, 72, 8730. We are after Evaluate √(11 + √72) + √(11 - √72). Tool of choice - sum of roots = 2×.3 = 6. Rearrange it for the unknown before substituting. Numbers in: √.72 = 6√.2 → 11±.6√.2 = (3±.√.2)^2 → sum of roots = 2×.3 = 6. Lock in option A) 6. Trap-watch: option B) '3' is wrong because √72 = 6√2; denest each term; option C) '11' is incorrect: Each root is 3±√2.

Q3. Evaluate √(18 + √128) + √(18 - √128).

• A.8
• B.4
• C.18
• D.9

Answer: A. 8

Given: 8730; 18; 8730; 128; 8730. We need: Evaluate √(18 + √128) + √(18 - √128). Governing law - sum of roots = 2×.4 = 8. This is the equation that links the given quantities to the unknown (math, chapter 'Number Systems'). Numerically: √.128 = 8√.2 → 18±.8√.2 = (4±.√.2)^2 → sum of roots = 2×.4 = 8. So the answer is A) 8. Where the distractors go off: option B) '4' is wrong because √128 = 8√2; denest each term; option C) '18' fails since Each root is 4±√2; option D) '9' misses the point - (4+√2)+(4-√2) = 8.