Square Root and Cube Root problems
- 1. The least perfect square, which is divisible by each of 21, 36 and 66 is:
Options- A. 213444
- B. 214344
- C. 214434
- D. 231444 Discuss
Correct Answer: 213444
Explanation:
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
- 2.
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.
- 3. 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 + √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
- 4. 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:
= √(1 - 2a)2 + 3a
= (1 - 2a) + 3a
= (1 + a)
= (1 + 0.1039)
= 1.1039
- 5. √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.
- 6. Find the cube root of 19683.
Options- A. 25
- B. 26
- C. 28
- D. 27 Discuss
Correct Answer: 27
Explanation:
In 19683, 19 lies between 23 and 33, so left digit is 2 and 683 ends with 3, so right digit is 7.
thus 27 is a cube root of 19683.
- 7. If ? y/169 = 54/39, then y is equal to?
Options- A. 108
- B. 324
- C. 2916
- D. 4800 Discuss
Correct Answer: 324
Explanation:
?y/169= 54/39
? y/169 = (54/39) x (54/39)
? y= (54/39) x (54/39) x 169 = 324
- 8. 112/?196 x ?579/12 x ?256/8 =?
Options- A. 8
- B. 12
- C. 16
- D. 32 Discuss
Correct Answer: 32
Explanation:
Given Expression 112/?196 x ?579/12 x ?256/8
=(112/14) x (24/12) x (16/8)
= 32
- 9. Given that ? 4096 = 64, the value of ? 4096 + ? 40.96 + ? .004096 is?
Options- A. 70.4
- B. 70.464
- C. 71.104
- D. 71.4 Discuss
Correct Answer: 70.464
Explanation:
?4096 + ?40.96 + ?.004096
= ?4096 + ?4096/100 + ?4096/1000000
=?4096 + ?4096/10 + ?4096/1000
= 64 + 64/10 + 64/1000
= 70.464
- 10. ? .04
Options- A. .02
- B. .2
- C. .002
- D. None of these Discuss
Correct Answer: .2
Explanation:
?.04 = ?4/100
= 2/10
= 0.2
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