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Square Root of 41
Did you know that the sum of the first six prime numbers, 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 particularly, the "atoms" of mathematics. Let us determine the square root of 41 in this article.
 Square Root of 41: √41 = 6.40312423743
 Square of 41: 41^{2} = 1681
What Is the Square Root of 41?
Let us look at an example of perfect squares 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 nonsquare numbers cannot have a square root? Nonsquare numbers also have a square root, but they are not whole numbers.
Square Root of 41
Square root of 41 in the radical form is expressed as √41 and in the exponent form, it is expressed as 41^{½}. The square root of 41, rounded to 5 decimal places, is ± 6.40312.
Is the Square Root of 41 Rational or Irrational?
A number that cannot be expressed as a ratio of two integers is an irrational number. The decimal form of the irrational number will be nonterminating (i.e. it never ends) and nonrecurring (i.e. the decimal part of the number never repeats a pattern). Now let us look at the square root of 41.
 √41 = 6.40312423743
Do you think the decimal part stops after 6.40312423743? No, it is neverending and you cannot observe any pattern in the decimal part.
Thus, √41 is an irrational number.
How to Find the Square Root of 41?
Square roots can be calculated using various methods, such as:
 By simplifying the radical of the numbers that are perfect squares.
 By long division method for perfect and nonperfect squares
41 is a prime number and hence, it is not a perfect square. Therefore, the square root of 41 can only be found by the long division method.
Simplified Radical Form of Square Root of 41
To simplify the square root of 41, let us first express 41 as the product of its prime factors. Prime factorization of 41 = 1 × 41. Therefore, √41 is in the lowest form and cannot be simplified further. Thus, we have expressed the square root of 41 in the radical form. Can you try and express the square root of 29 in a similar way?
Square Root of 41 By Long Division Method
Let us follow these steps to find the square root of 41 by long division.
 Step 1: Group the digits into pairs (for digits to the left of the decimal point, pair them from right to left) by placing a bar over it. Since our number is 41, let us represent it inside the division symbol.
 Step 2: Find the largest number such that when you multiply it with itself, the product is less than or equal to 41. We know that 6 × 6 = 36 and is less than 41. Now, let us divide 41 by 6.
 Step 3: Let us place 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: Choose a number in the unit's place for the new divisor such that its product with a number is less than or equal to 500. We know that 2 is in the ten's place and our product has to be 500 and the closest multiplication is 124 × 4 = 496.
 Step 5: Bring down the next pair of zeros and multiply the quotient 64 (ignore the decimal) by 2, which is 128. This number forms the starting digits of the new divisor.
 Step 6: Choose the largest digit in the unit's place for the new divisor such that the product of the new divisor with the digit at one's place is less than or equal to 400. We see that 1281, when multiplied by 1, gives 1281 which is greater than 400. Therefore, we will take 1280 × 0 = 0 which is less than 400.
 Step 7: Add more pairs of zeros and repeat the process of finding the new divisor and product as in step 2.
Note that the square root of 41 is an irrational number, i.e. it is neverending. So, you can stop the process after 4 or 5 iterations.
Explore square roots using illustrations and interactive examples
Important Notes:
 The square root of 41 in the radical form is expressed as √41
 In exponent form, the square root of 41 is expressed as 41^{½}.
 The real roots of √41 are ± 6.40312.
Challenging Questions:
 What is the value of √√√√41?
 Simplify ((41)^{½})^{¾}
 Determine the square root of 4141.
Square Root of 41 Solved Examples

Example 1: Fredrick told his friends that the value of √41 is the same as √41. What do you think?
Solution
Negative square root cannot be real numbers.
√41 is a real number.
But √41 is an imaginary number.
Hence, they are not the same. √41 is not the same as √41. 
Example 2
Joel had a doubt. He knew that 6.403 is the square root of 41. He wanted to know if 6.403 is also a square root of 41? Can you clarify his doubt?
Solution:
Let us take an example of a perfect square number and extend the same logic to clarify Joel's doubt.
We know that 3 is a square root of 9 because when 3 is multiplied to itself it gives 9. But, what about 3? Let us multiply and check.
3 × 3 = 9 ( ×  = +)
Therefore, 3 is also a square root of 9. Thus, 6.403 is also the square root of 41. 
Example 3
Help Tim simplify √√41.
Solution:
By long division, we learnt that √41 = 6.403.
We need to find the value of √6.403. Going by the same long division steps as discussed above, we get √6.403 = 2.530.
FAQs on Square Root of 41
What is the square root of 41?
Square root of 41: √41 = 6.40312423743.
What is the square of 41?
Square of 41 is 1681.
How do you work out the square root of 41?
We can find the square root of 41 using various methods.
 Repeated Subtraction
 Prime Factorization
 Estimation and Approximation
 Long Division
If you want to learn more about each of these methods, click here.
How do you find √41 times √41?
The value of √41 × √41 = 41
What is the square root of 41 in the simplest radical form?
√41 is the simplest radical form.
Is the square root of 41 an irrational number?
√41 = 6.40312423743
√41 is an irrational number.
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