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- Question
The least perfect square, which is divisible by each of 21, 36 and 66 is:
Options- A. 213444
- B. 214344
- C. 214434
- D. 231444
- Correct Answer
- 213444
ExplanationL.C.M. of 21, 36, 66 = 2772.Now, 2772 = 2 x 2 x 3 x 3 x 7 x 11
To make it a perfect square, it must be multiplied by 7 x 11.
So, required number = 22 x 32 x 72 x 112 = 213444
Square Root and Cube Root problems
Search Results
- 1.
❨ √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 - 2. 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. - 3. 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.- 4. √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 - 5.
❨ √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 - 6.
What should come in place of both x in the equation x = √162 . √128 x
Options- A. 12
- B. 14
- C. 144
- D. 196 Discuss
Correct Answer: 12
Explanation:
Let x = √162 √128 x Then x2 = √128 x 162
= √64 x 2 x 18 x 9
= √82 x 62 x 32
= 8 x 6 x 3
= 144.
∴ x = √144 = 12.
- 7. If 3√5 + √125 = 17.88, then what will be the value of √80 + 6√5?
Options- A. 13.41
- B. 20.46
- C. 21.66
- D. 22.35 Discuss
Correct Answer: 22.35
Explanation:
3√5 + √125 = 17.88⟹ 3√5 + √25 x 5 = 17.88
⟹ 3√5 + 5√5 = 17.88
⟹ 8√5 = 17.88
⟹ √5 = 2.235
∴ √80 + 6√5 = √16 x 5 + 6√5
= 4√5 + 6√5
= 10√5 = (10 x 2.235) = 22.35
- 8. If a = 0.1039, then the value of √4a2 - 4a + 1 + 3a is:
Options- A. 0.1039
- B. 0.2078
- C. 1.1039
- D. 2.1039 Discuss
Correct Answer: 1.1039
Explanation:
√4a2 - 4a + 1 + 3a = √(1)2 + (2a)2 - 2 x 1 x 2a + 3a= √(1 - 2a)2 + 3a
= (1 - 2a) + 3a
= (1 + a)
= (1 + 0.1039)
= 1.1039
- 9. √1.5625 =?
Options- A. 1.05
- B. 1.25
- C. 1.45
- D. 1.55 Discuss
Correct Answer: 1.25
Explanation:
1|1.5625( 1.25 |1 |------- 22| 56 | 44 |------- 245| 1225 | 1225 |------- | X |-------∴ √1.5625 = 1.25.- 10. The sum of three numbers is 98. If the ratio of the first to second is 2 :3 and that of the second to the third is 5 : 8, then the second number is:
Options- A. 20
- B. 30
- C. 48
- D. 58 Discuss
Correct Answer: 30
Explanation:
Let the three parts be A, B, C. Then,A : B = 2 : 3 and B : C = 5 : 8 = ❨ 5 x 3 ❩ : ❨ 8 x 3 ❩ = 3 : 24 5 5 5 ⟹ A : B : C = 2 : 3 : 24 = 10 : 15 : 24 5 ⟹ B = ❨ 98 x 15 ❩ = 30. 49
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