Square Root and Cube Root problems
- 1. 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
- 2. 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.
- 3.
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 Discuss
Correct Answer: 14
Explanation:
| x = | (√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
- 4. 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.
- 5.
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 |
- 6.
❨ √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 |
- 7. √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 |
- 8. 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.
- 9. The square root of (7 + 3√5) (7 - 3√5) is
Options- A. √5
- B. 2
- C. 4
- D. 3√5 Discuss
Correct Answer: 2
Explanation:
| (7 + 3√5)(7 - 3√5) | = | (7)2 - (3√5)2 | = √49 - 45 = √4 = 2. |
- 10.
❨ √3 - 1 ❩ 2 simplifies to: √3
Options- A.
3 4 - B.
4 √3 - C.
4 3 - D. None of these Discuss
Correct Answer:
| 4 |
| 3 |
Explanation:
| ❨ | √3 - | 1 | ❩ | 2 | = (√3)2 + | ❨ | 1 | ❩ | 2 | - 2 x √3 x | 1 |
| √3 | √3 | √3 |
| = 3 + | 1 | - 2 |
| 3 |
| = 1 + | 1 |
| 3 |
| = | 4 |
| 3 |
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