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What is the cube root of 21952?
  • a)
    26
  • b)
    28
  • c)
    24
  • d)
    32
Correct answer is option 'B'. Can you explain this answer?

Parth Joshi answered
Understanding the Cube Root
The cube root of a number x is a value y such that y multiplied by itself three times equals x, or mathematically, y^3 = x. In this case, we want to find the cube root of 21952.
Calculating the Cube Root of 21952
To find the cube root of 21952, we can use prime factorization or estimation:
  • First, we can estimate the cube root by comparing it to nearby perfect cubes. For example:

    • 20^3 = 8000
    • 30^3 = 27000
  • Since 21952 is between these two values, we can narrow it down further.

Finding the Exact Value
Now, let's find the cube root more accurately:
  • We can start testing integers around our estimate:

    • 25^3 = 15625 (too low)
    • 26^3 = 17576 (still too low)
    • 27^3 = 19683 (close but still low)
    • 28^3 = 21952 (correct)


Conclusion
Through estimation and testing, we find that:
  • The cube root of 21952 is 28.
  • Therefore, the correct answer is option 'B'.

Understanding cube roots involves both estimation and verification through calculation, leading us to the conclusion that the cube root of 21952 is indeed 28.

Find the square root of 21904.
  • a)
    146
  • b)
    148
  • c)
    152
  • d)
    156
Correct answer is option 'B'. Can you explain this answer?

To find the square root of 21904:
  • We can calculate by multiplying numbers.
  • Testing 148:
    • 148 * 148 = 21904
The square root of 21904 is 148.

What is the cube root of 493039?
  • a)
    77
  • b)
    79
  • c)
    81
  • d)
    83
Correct answer is option 'B'. Can you explain this answer?

The cube root of 493039 is calculated as follows:
  • To find the cube root, we need to determine a number that, when multiplied by itself three times, equals 493039.
  • After testing various numbers, we find:
  • 79 * 79 * 79 = 493039.
Thus, the cube root of 493039 is 79.

What is the cube root of 175616?
  • a)
    52
  • b)
    54
  • c)
    56
  • d)
    58
Correct answer is option 'C'. Can you explain this answer?

Aim It Academy answered
The cube root of 175616 is 56.
To verify this result:
  • Calculate 56 multiplied by itself three times:
  • 56 × 56 × 56 = 175616
Thus, the calculation confirms that the cube root is indeed 56.

Find the square root of 6241.
  • a)
    77
  • b)
    79
  • c)
    81
  • d)
    83
Correct answer is option 'B'. Can you explain this answer?

Aim It Academy answered
The square root of 6241 is calculated as follows:
  • To find the square root, we need to determine a number that, when multiplied by itself, equals 6241.
  • After checking various possibilities, we find that 79 multiplied by 79 equals 6241.
Therefore, the square root of 6241 is 79.

Find the square root of 32041.
  • a)
    177
  • b)
    179
  • c)
    181
  • d)
    183
Correct answer is option 'B'. Can you explain this answer?

To find the square root of 32041:
  • First, we will test the number 179.
  • Calculate: 179 * 179.
  • The result is 32041.
This confirms that the square root of 32041 is 179.

Find the square root of 10609.
  • a)
    101
  • b)
    103
  • c)
    107
  • d)
    109
Correct answer is option 'B'. Can you explain this answer?

Aim It Academy answered
The square root of 10609 is calculated as follows:
  • To find the square root, we can check if a number multiplied by itself equals 10609.
  • By testing, we find that 103 multiplied by 103 equals 10609.
  • Therefore, the square root of 10609 is 103.

Find the square root of 15129.
  • a)
    121
  • b)
    123
  • c)
    127
  • d)
    129
Correct answer is option 'B'. Can you explain this answer?

To find the square root of 15129:
  • We need to identify a number that, when multiplied by itself, equals 15129.
  • Calculating, we find:
    • 123 * 123 = 15129
  • Thus, the square root of 15129 is 123.

What is the cube root of 97336?
  • a)
    44
  • b)
    46
  • c)
    48
  • d)
    52
Correct answer is option 'B'. Can you explain this answer?

The cube root of 97336 is 46.
To find this, we can multiply:
  • 46 multiplied by 46 gives 2116.
  • Then, multiplying 2116 by 46 results in 97336.
Thus, the cube root of 97336 is confirmed to be 46.

What is the cube root of 681472?
  • a)
    86
  • b)
    88
  • c)
    92
  • d)
    96
Correct answer is option 'B'. Can you explain this answer?

The cube root of 681472 is 88.
To confirm this, we can calculate:
  • 88 multiplied by 88 equals 7744.
  • Next, 7744 multiplied by 88 equals 681472.
Thus, the cube root is correctly determined to be 88.

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