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Home ‣ Aptitude ‣ Square Root and Cube Root Comments
- Question
The square root of 64009 is:
Options- A. 253
- B. 347
- C. 363
- D. 803
- Correct Answer
- 253
Explanation2|64009( 253 |4 |---------- 45|240 |225 |---------- 503| 1509 | 1509 |---------- | X |----------∴ √64009 = 253.
Square Root and Cube Root problems
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- 1. √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 - 2.
❨ √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 - 3.
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 - 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 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
- 6. 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. - 7.
❨ √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 - 8. 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:
L.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
- 9.
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.
- 10. 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
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