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Home ‣ Aptitude ‣ Square Root and Cube Root Comments
- Question
If x = √3 + 1 and y = √3 - 1 , then the value of (x2 + y2) is: √3 - 1 √3 + 1
Options- A. 10
- B. 13
- C. 14
- D. 15
- Correct Answer
- 14
Explanationx = (√3 + 1) x (√3 + 1) = (√3 + 1)2 = 3 + 1 + 2√3 = 2 + √3. (√3 - 1) (√3 + 1) (3 - 1) 2 y = (√3 - 1) x (√3 - 1) = (√3 - 1)2 = 3 + 1 - 2√3 = 2 - √3. (√3 + 1) (√3 - 1) (3 - 1) 2 ∴ x2 + y2 = (2 + √3)2 + (2 - √3)2
= 2(4 + 3)
= 14
Square Root and Cube Root problems
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- 1. 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. 59.29, the number of the member is the group is:
Options- A. 57
- B. 67
- C. 77
- D. 87 Discuss
Correct Answer: 77
Explanation:
Money collected = (59.29 x 100) paise = 5929 paise.∴ Number of members = √5929 = 77.
- 2. The cube root of .000216 is:
Options- A. .6
- B. .06
- C. 77
- D. 87 Discuss
Correct Answer: .06
Explanation:
(.000216)1/3 = ❨ 216 ❩ 1/3 106 = ❨ 6 x 6 x 6 ❩ 1/3 102 x 102 x 102 = 6 102 = 6 100 = 0.06
- 3.
The fraction 101 27 in decimal for is: 100000
Options- A. .01027
- B. .10127
- C. 101.00027
- D. 101.000027 Discuss
Correct Answer: 101.00027
Explanation:
101 27 = 101 + 27 = 101 + .00027 = 101.00027 100000 100000 - 4.
The value of 0.1 x 0.1 x 0.1 + 0.02 x 0.02 x 0.02 is: 0.2 x 0.2 x 0.2 + 0.04 x 0.04 x 0.04
Options- A. 0.0125
- B. 0.125
- C. 0.25
- D. 0.5 Discuss
Correct Answer: 0.125
Explanation:
Given expression = (0.1)3 + (0.02)3 = 1 = 0.125 23 [(0.1)3 + (0.02)3] 8 - 5. 34.95 + 240.016 + 23.98 =?
Options- A. 298.0946
- B. 298.111
- C. 298.946
- D. 299.09 Discuss
Correct Answer: 298.946
Explanation:
34.95 240.016 + 23.98 -------- 298.946 --------
- 6. How many two-digit numbers satisfy this property.: The last digit (unit's digit) of the square of the two-digit number is 8?
Options- A. 1
- B. 2
- C. 3
- D. None of these Discuss
Correct Answer: None of these
Explanation:
A number ending in 8 can never be a perfect square.- 7.
If √5 = 2.236, then the value of √5 - 10 + √125 is equal to: 2 √5
Options- A. 5.59
- B. 7.826
- C. 8.944
- D. 10.062 Discuss
Correct Answer: 7.826
Explanation:
√5 - 10 + √125 = (√5)2 - 20 + 2√5 x 5√5 2 √5 2√5 = 5 - 20 + 50 2√5 = 35 x √5 2√5 √5 = 35√5 10 = 7 x 2.236 2 = 7 x 1.118 = 7.826 - 8.
❨ √625 x 14 x 11 ❩ is equal to: 11 √25 √196
Options- A. 5
- B. 6
- C. 8
- D. 11 Discuss
Correct Answer: 5
Explanation:
Given Expression = 25 x 14 x 11 = 5. 11 5 14 - 9. √0.0169 x? = 1.3
Options- A. 10
- B. 100
- C. 1000
- D. None of these Discuss
Correct Answer: 100
Explanation:
Let √0.0169 x x = 1.3.Then, 0.0169x = (1.3)2 = 1.69
⟹ x = 1.69 = 100 0.0169 - 10. The square root of 64009 is:
Options- A. 253
- B. 347
- C. 363
- D. 803 Discuss
Correct Answer: 253
Explanation:
2|64009( 253 |4 |---------- 45|240 |225 |---------- 503| 1509 | 1509 |---------- | X |----------∴ √64009 = 253.
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