Square Root and Cube Root problems
- 1. 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
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.
- 2. ? 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
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
- 3. The least perfect square number divisible by 3, 4, 5, 6, 8 is?
Options- A. 900
- B. 1200
- C. 2500
- D. 3600 Discuss
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
- 4. (? 5 - ? 3)/ (? 5 + ? 3) is equal to?
Options- A. 4 + ?15
- B. 4 - ?15
- C. 1/2
- D. 1 Discuss
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)
- 5. 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 Also asked in: AIEEE, Bank Exams, CAT, Bank Clerk, Bank PO
Correct Answer: 4/3
Explanation:
a = [(?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
- 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
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 .
- 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
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.
- 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
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
- 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
Correct Answer: 47
Explanation:
Number of members = ?2209
= 47
- 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
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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