Square Root and Cube Root problems
- 1. ? 248 + ?(52+ ?144)
Options- A. 14
- B. 16
- C. 16.6
- D. 18.8 Discuss
Correct Answer: 16
Explanation:
?248 + ?(52 + ?144)
= ?248 + ?(52 + 12)
=?248 + ?64
= ?248 + 8
= ?256
= 16
- 2. ? 176 + ?2401 =?
Options- A. 14
- B. 15
- C. 18
- D. 24 Discuss
Correct Answer: 15
Explanation:
?176 + ?2401
= ?176 + 49
= ?225 = 15
- 3. (? 32 + ? 48) / (? 8 + ? 12) =?
Options- A. ?2
- B. 2
- C. 4
- D. 8 Discuss
Correct Answer: 2
Explanation:
(?32 + ?48) / (?8 + ?12)
= (?16 x 2 + ?16 x 3) / (?4 x 2 + ?4 x 3)
= (4?2 + 4?3) / (2?2 + 2?3)
= 4(?2 + ?3) / 2(?2 + ?3 ) = 2
- 4. If ? 3 =1.732 and ? 2 = 1.414, the value of 1/(? 3 + ? 2) is?
Options- A. 0.064
- B. 0.308
- C. 0.318
- D. 2.146 Discuss
Correct Answer: 0.318
Explanation:
1/ (?3 + ?2)
= (?3 - ?2) / [ 1/ (?3 - ?2) x (?3 + ?2)]
= (?3 - ?2) / (3 - 2)
= (1.7732 - 1.414) = 0.318
- 5. If ? 6 = 2.55, then the value of ? 2/3 + 3 ? 3/2 is?
Options- A. 4.48
- B. 4.49
- C. 4.50
- D. None of these Discuss
Correct Answer: None of these
Explanation:
=?2/3 + 3?3/2
= ?2/?3 x ?3/?3 + 3?3/?2 x ?2/ ?2
= ?6/3 + 3?6/2
= (2.55 / 3) + [(3 x 2.55) / 2]
= 2.55/3 + 7.65/2
= (5.10 + 22.95)/6
= 28.05/6
= 4.675
- 6. If ? 2 n = 64, then the value of n is?
Options- A. 2
- B. 4
- C. 6
- D. 12 Discuss
Correct Answer: 12
Explanation:
?2n = 64
? 2n/2 = 26
? n/2 = 6
? n = 12
- 7. ? (1.21 x 0.9) / (1.1 x 0.11) =?
Options- A. 2
- B. 3
- C. 9
- D. 11 Discuss
Correct Answer: 3
Explanation:
Given expression = ?(121 x 9) / (11 x 11)
= ?9
= 3
- 8. If ? 1 + 27/169) = (1 + N/13). then N equals?
Options- A. 1
- B. 3
- C. 5
- D. 7 Discuss
Correct Answer: 1
Explanation:
?1 + 27/169 = (1 + N/13)
? ?196/169 = (1 + N/13)
? 14/13 = (1 + N/13)
? N/13 = (14/13 - 1 ) = 1/13
? N = 1
- 9. ?( 12 + ?12 + ?12 + ... =?
Options- A. 3
- B. 4
- C. 6
- D. Greater than 6 Discuss
Correct Answer: 4
Explanation:
Let given expression = x
Then, ?12 + x = x
? 12 + x = x2
? x2 - x - 12 = 0
? (x - 4) (x + 3) = 0
So, x = 4 (neglecting x = -3)
- 10. If ? 2 = 1.4142, the value of 7/ (3 + ? 2) is?
Options- A. 1.5858
- B. 4.4142
- C. 3.4852
- D. 3.5858 Discuss
Correct Answer: 1.5858
Explanation:
7/(3 + ?2) = [7 x (3- ?2)] / [(3 + ?2) x (3- ?2)]
= [7 x ( (3- ?2)] / 7
= 3- ?2
= 3 - 1.4142
= 1.5858
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