Square Root of 841
841 is a perfect square number which is obtained by square of 29. Hence, the square root of 841 is a rational number. Square root is described with the symbol √. If n is an integer than square of n is equal to m which is also an integer. If n² = m, then n=√m. The square root of 841 is written as √841. Let us explore the square root of 841 in detail. 841 is a composite number, as it has more than 2 factors. In this minilesson we will learn to find square root of 841 along with solved examples. Let us see what the square root of 841 is.
 Square Root of 841: √841 = 29
 Square of 841: 841^{2} = 707,281
1.  What Is the Square Root of 841? 
2.  Is Square Root of 841 Rational or Irrational? 
3.  How to Find the Square Root of 841? 
4.  Important Notes 
5.  Thinking Out of the Box! 
5.  FAQs on Square Root of 841 
What Is the Square Root of 841?
The original number whose square is 841 gives the square root of 841.
√841 = 29
The answer which we get on squaring 29² is 841. This makes 841 a perfect square.
Is the Square Root of 841 Rational or Irrational?
A rational number can be either terminating or nonterminating and has a repeating pattern in its decimal part. We saw that √841 = 29. 29 is a whole number. It is possible to express it in p/q form easily. Hence, √841 is a rational number.
How to Find the Square Root of 841?
There are different methods to find the square root of any number. Click here to know more about it.
The factors of 841 are 1, 29, and 841.
As 841 has more than 2 factors, it is a composite number
To find the square root of 841:
 We can use prime factorization method to obtain one number from each pair of the same numbers and multiply them. The prime factorization of 841 is 29 × 29 which consists of 1 pair of the same number, 29. Thus, the square root of 841 = 29.
 Since 841 is a perfect square, we can also express it as 29^{2}. The number within square root which gets repeated is √(29 × 29) = 29. Hence, the square root of 841 is 29.
√841 = √29² = (29)^{2 × ½} = 29
The square root of 841 is 29.
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Important Notes:
 841 is a perfect square as the answer obtained after square root is a rational number.
 The square root of 841 can be simplified to 29 either by using the prime factorization of 841 or by expressing 841 as a square of 29.
Think Tank:
 Can the value of a square root of 841 be decimal?
 Is √841 a real number?
Square Root of 841 Solved Examples

Example 1: What is the difference in lengths of square boxes having area 841 square inches and 729 square inches ?
Solution
As the area of square box is area = length × length
The length of square box having area 841 square inches is √841 = 29 inches.
Similarly the length of box having area 729 square inches is √729 = 27 inches.
The difference in lengths of boxes is (29  27) inches = 2 inches
Hence, the difference in length of square boxes having area 841 square inches and 729 square inches is 2 inches. 
Example 2: Can you determine the radius of circle having area 841π square inches?
Solution
Radius can be found using the formula of area of a circle is πr^{2} square inches. By the given information,
πr^{2} = 841π
r^{2} = 841
By taking the square root on both sides we get, √r^{2}= √841. We know that the square root of r^{2} is r.
By calculating the square root of 841 is 29 inches. 
Example 3: Can you determine the square root of 841 using long division method?
Solution
To find the square root of 841 using long division method we need to follow the following steps:
 Step1. Write 841 as shown in the figure. Start pairing the digits from the right end in pairs of two by putting a bar on top of them. So, we got two pairs of 8 and 41
 Step2. Now find a number (q) such that q × q is a number less than equal to 8. Hence, q = 2 (2 × 2 = 4).
 Step3. Now subtract the obtained value from the first pair in the dividend and add the divisor with itself (q + q) (2 + 2 = 4). Now bring the second pair down (41). The remiander is 441.
 Step4. Now find a number (p) such that 2p × p is less than equal to 441. Here m will be 9 as 49 × 9 = 441.
FAQs On Square Root of 841
What are the two square roots of 841?
The square roots of 841 are 29 and 29.
Is 841 a perfect square?
Yes, 841 is a perfect square
Does 841 have a square root?
Yes, 841 has a square root
Can square root of 841 simplified?
841 can be broken down as a product of 27 × 29. Either ways, the square root of 841 gives output as 29.
Is the square root of 841 rational or irrational?
The square root of 841 is rational.
Is square root of 841 a real number?
Yes, the square root of 841 is a real number.