# Square Root of 41 | Top Q&A

Square Root of 41 Did you know that the sum of the first six primes, i.e., 2, 3, 5, 7, 11 and 13 is 41? 41 is an odd prime number. Prime numbers have been described as the building blocks of mathematics, or more specifically, as the “atoms” of mathematics. Let us determine the square root of 41 in this article.

**Square root of 41**: 41 = 6.40312423743**Square 41: 412**= 1681

1. What is the square root of 41? 2. Is the square root of 41 Reasonable or Unreasonable? 3. How to find the square root of 41? 4. Frequently Asked Questions about Square Root of 60 5. Important Notes 6. Tough Questions 7. Frequently Asked Questions about Square Root of 41 Let’s see an example of shapes perfect square first. 3² = 3 × 3 = 9 is an example. Here 3 is called the square root of 9, but 9 is a perfect square. Does that mean zero squared numbers can’t have square roots? Non-squared numbers also have square roots, but they are not integers.

### Square root of 41

The square root of 41 in root form is represented by √41, and in power form it is represented by 41½. The square root of 41, rounded to 5 decimal places is ±6.40312. A number that cannot be expressed as a ratio of two integers is an irrational number. The decimal form of an irrational number is non-terminating (i.e. it never ends) and non-repeating (i.e. the decimal part of the number never repeats a pattern). Now let’s look at the square root of 41. Do you think the decimal part stops after 6.40312423743? No, it’s never ending and you can’t observe any patterns in the decimal part, so √41 is an irrational number.

- By simplifying the roots of the numbers are perfect squares.
- By dividing length by perfect and imperfect squares

41 is a prime number and therefore it is not a perfect square. Therefore, the square root of 41 can only be found by the long division method.

### Simple square root form of square root 41

To simplify the square root of 41, let’s first express 41 as a product of its prime factors. The prime factor of 41 = 1 × 41. Therefore, √41 is in its lowest form and cannot be further simplified. Thus, we have represented the square root of 41 in root form. Can you try and represent the square root of 29 in a similar way?

### Square root of 41 by length division

Let’s follow these steps to find the square root of 41 for long division.

- Step 1: Group the digits into pairs (for digits to the left of the decimal point, pair them right to left) by placing a bar over it. Since our number is 41, let us represent it inside division notation.
- Step 2: Find the largest number such that when multiplied by itself the product is less than or equal to 41. We know 6 × 6 = 36 and less than 41. Now, we divide 41 by 6.
- Step 3: Let’s put a decimal point and pairs of zeros and continue our division. Now, multiply the quotient by 2 and the product becomes the starting digits of our next divisor.
- Step 4: Pick a number in the units row to divide so that its product with a number is less than or equal to 500. We know that 2 is in the place of ten and our product should be 500 and the nearest multiplication is 124 × 4 = 496.
- Step 5: Reduce the next pair of zeros and multiply the quotient 64 (ignoring the decimals) by 2, giving 128. This number forms the starting digits of the new divisor.
- Step 6: Choose the largest digit in the units row for the new divisor so that the product of the new divisor and the digit in one’s place is less than or equal to 400. We see that 1281 when multiplied by 1 gives 1281 which greater than 400. Therefore, we will take 1280 × 0 = 0 less than 400.
- Step 7: Add more pairs of zeros and repeat the process of finding new divisors and products as in step 2.

Note that the square root of 41 is an irrational number, which means it never ends. So you can stop the process after 4 or 5 iterations.**Explore square roots using interactive illustrations and examples**

- Square root of 44
- Square root of 54
- Square root of 56
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- Square root of 34

- The square root of 41 in root form is expressed as 41
- In exponentiation, the square root of 41 is expressed as 41½.
- The real roots of √41 are ±6.40312.

- What is the value of √√√√41?
- Simplify ((41) ) ¾
- Determine the square root of 4141.

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