Discussion
Home ‣ Aptitude ‣ Square Root and Cube Root Comments
- Question
- If a = (? 5 + 1) / (? 5 - 1) and b = (? 5 - 1) / ( ? 5 + 1) then the value of (a 2 + ab + b 2) / (a 2 - ab + b 2) is?
Options- A. 3/4
- B. 4/3
- C. 3/5
- D. 5/3
- Correct Answer
- 4/3
Explanationa = [(?5 + 1) / (?5-1)] x [(?5 + 1) / (?5 + 1)]
= (?5 + 1)2 / (5 - 1)
= (5 + 1 + 2 ?5) / 4
= (3 + ?5) / 2
b = [(?5 - 1) / (?5 + 1)] x [(?5 - 1 ) / (?5 -1)]
= (?5 - 1 )2 / (5 - 1)
= (5 + 1 - 2?5) / 4
= (3 - ?5) / 2
Now a2 + b2 = [(3 + ?5)2 + (3 - ?5)2] / 4
= [2 x (9 + 5 )] / 4
= 7
ab = 1
? (a2 + ab + b2) / (a2 - ab + b2)
= (7 + 1) / (7 - 1)
= 8/6
= 4 / 3 - 1. (? 5 - ? 3)/ (? 5 + ? 3) is equal to?
Options- A. 4 + ?15
- B. 4 - ?15
- C. 1/2
- D. 1 Discuss
- 2. The least perfect square number divisible by 3, 4, 5, 6, 8 is?
Options- A. 900
- B. 1200
- C. 2500
- D. 3600 Discuss
- 3. ? 0.04 x 0.4 x a = 0.4 x 0.04 x ? b, then the value of a/b is?
Options- A. 0.016
- B. 1.60
- C. 0.16
- D. None of these Discuss
- 4. Which of the following numbers, Where in some of the digit have been suppressed by Symbols, can possibly be the perfect square of a 3 digit odd number.?
Options- A. 65xxx1
- B. 9xx1
- C. 10xxx4
- D. 9xxxxxx5 Discuss
- 5. 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
- 6. The least number by which 216 must be divided to make the result a perfect square is?
Options- A. 3
- B. 4
- C. 6
- D. 9 Discuss
- 7. The least number by which 176 be multiplied to make the result a perfect square is?
Options- A. 8
- B. 9
- C. 10
- D. 11 Discuss
- 8. The length of diagonal of a square is 8 cm. The length of the side of the square is?
Options- A. 2 cm
- B. 2.8 cm
- C. 1.414 cm
- D. 5.64 cm Discuss
- 9. A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 22.09, the number of members in the group is?
Options- A. 37
- B. 47
- C. 107
- D. 43 Discuss
- 10. The square root of (1/4) x (1/49) ÷ (25/121) is
Options- A. 11/5
- B. 11/70
- C. 7/11
- D. 11/7 Discuss
Square Root and Cube Root problems
Search Results
Correct Answer: 4 - ?15
Explanation:
(?5 - ?3)/ (?5 + ?3)
= (?5 - ?3) / (?5 + ?3)
= (?5 - ?3)2 / (5 - 3)
= (5 + 3 - 2?5 x 3) / 2
= 2 (4 - ?15) / 2
= (4 - ?15)
Correct Answer: 3600
Explanation:
L. C. M of 3, 4, 5, 6, 8 is 120
Now, 120 = 2 x 2 x 2 x 3 x 5
? Required number = (2 x 2 x 2 x 3 x 5) x (2 x 3 x 5)
= 3600
Correct Answer: 0.016
Explanation:
?0.04 x 0.4 x a = 0.4 x 0.04 x ?b
? ?0.016 a = 0.016 x ?b
? ?a / ?b = 0.016/?0.016 = ?0.016
? ?a/b = ?0.016
So a/b = 0.016
Correct Answer: 65xxx1
Explanation:
The square of an odd number cannot have 4 as the unit digit. The square of a 3 digit number will have at least 5 digit and at the most 6 digits. So. answer (A) is correct.
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
Correct Answer: 6
Explanation:
216 = 2 x 2 x 2 x 3 x 3 x 3
= (2 x 2) x 2 x ( 3 x 3) x 3
Clearly, in order to make it a perfect square, it must be divided by 2 x 3 i.e., 6 .
Correct Answer: 11
Explanation:
176 = 2 x 2 x 2 x 2 x 11
So, in order to make it a perfect square, it must be multiplied by 11.
Correct Answer: 5.64 cm
Explanation:
a2 + a2 = (8)2
? 2a2 = 64
? a2 = 32
? a = ?32 = 4?2
= 4 x 1.41
= 5.64 cm
Correct Answer: 47
Explanation:
Number of members = ?2209
= 47
Correct Answer: 11/70
Explanation:
Square root of (1/4) x (1/49) ÷ (25/121)
= ?(1/4) x (1/49) x (121/25)
= 11 / (2 x 7 x 5)
= 11/70
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