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The square root of 16641 is
- a)129
- b)121
- c)211
- d)229
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The square root of 16641 isa)129b)121c)211d)229Correct answer is optio...
Step 1:
- We now need to obtain the digital root of the number. Here's how you do it:
- Split the number up and add each digit together:
1 + 6 + 6 + 4 + 1 = 18 - If the answer is more than one digit, you would add each digit of the answer together again:
1 + 8 = 9 - What is the digital root of number 16,641?
Answer: 9
Step 2:
- So now we know the digital root of 16,641 is 9. Is 9 in the list of digital roots that are always a square root (1, 4, 7 or 9)?
- Answer: YES, 9 is in the list of digital roots that are always perfect squares. We can conclude that 16,641 could be a perfect square!
Factoring
- OK, so now we know that 16,641 could be a perfect square. We have to find the factors of the number to be sure.
- Here are all of the factors of 16,641:
(1 x 16,641) (3 x 5,547) (9 x 1,849) (43 x 387) (129 x 129)
Hence the answer is 129.
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The square root of 16641 isa)129b)121c)211d)229Correct answer is optio...
The square root of 16641 is 129.
To find the square root of 16641, we can use various methods like prime factorization, long division, or a calculator. Let's use the prime factorization method to explain the answer.
Prime Factorization of 16641:
1. Start by finding the prime factors of the given number.
2. Divide the number by the smallest prime number possible, which is 2. But 16641 is an odd number, so it is not divisible by 2.
3. The next prime number is 3. Divide 16641 by 3.
16641 ÷ 3 = 5547
4. The division results in an integer, so 3 is a factor. Continue dividing the quotient by 3.
5547 ÷ 3 = 1849
5. Again, the division results in an integer. Continue dividing by 3.
1849 ÷ 3 = 617
6. The process continues until we reach a point where we cannot divide any further.
617 is a prime number.
Therefore, the prime factorization of 16641 is 3 × 3 × 3 × 617.
Identifying Perfect Squares:
To find the square root, we need to identify the perfect squares that can be formed using the prime factors of 16641.
The prime factors are 3 × 3 × 3 × 617.
We can group the prime factors into pairs of 2:
(3 × 3) × (3 × 617)
Simplifying further:
(3 × 3) = 9
(3 × 617) = 1851
We can see that 3 × 3 = 9 is a perfect square, but 3 × 617 = 1851 is not a perfect square.
Calculating the Square Root:
Now, let's calculate the square root using the identified perfect square.
√16641 = √(9 × 1851)
We can split the square root of a product into the product of the square roots:
√(9 × 1851) = √9 × √1851
√9 = 3
Therefore, the square root of 16641 is 3√1851.
Calculating the Cube Root:
Now, we need to calculate the cube root of 1851.
By trial and error, we can find that the cube root of 1851 is approximately 12.999 or 13.
Therefore, the square root of 16641 is approximately 3 × 13 = 39.
Hence, the correct answer is option A) 129.
To find the square root of 16641, we can use various methods like prime factorization, long division, or a calculator. Let's use the prime factorization method to explain the answer.
Prime Factorization of 16641:
1. Start by finding the prime factors of the given number.
2. Divide the number by the smallest prime number possible, which is 2. But 16641 is an odd number, so it is not divisible by 2.
3. The next prime number is 3. Divide 16641 by 3.
16641 ÷ 3 = 5547
4. The division results in an integer, so 3 is a factor. Continue dividing the quotient by 3.
5547 ÷ 3 = 1849
5. Again, the division results in an integer. Continue dividing by 3.
1849 ÷ 3 = 617
6. The process continues until we reach a point where we cannot divide any further.
617 is a prime number.
Therefore, the prime factorization of 16641 is 3 × 3 × 3 × 617.
Identifying Perfect Squares:
To find the square root, we need to identify the perfect squares that can be formed using the prime factors of 16641.
The prime factors are 3 × 3 × 3 × 617.
We can group the prime factors into pairs of 2:
(3 × 3) × (3 × 617)
Simplifying further:
(3 × 3) = 9
(3 × 617) = 1851
We can see that 3 × 3 = 9 is a perfect square, but 3 × 617 = 1851 is not a perfect square.
Calculating the Square Root:
Now, let's calculate the square root using the identified perfect square.
√16641 = √(9 × 1851)
We can split the square root of a product into the product of the square roots:
√(9 × 1851) = √9 × √1851
√9 = 3
Therefore, the square root of 16641 is 3√1851.
Calculating the Cube Root:
Now, we need to calculate the cube root of 1851.
By trial and error, we can find that the cube root of 1851 is approximately 12.999 or 13.
Therefore, the square root of 16641 is approximately 3 × 13 = 39.
Hence, the correct answer is option A) 129.
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The square root of 16641 isa)129b)121c)211d)229Correct answer is option 'A'. Can you explain this answer?
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