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Square Root of 841 + Solution With Free Steps
√841 is the mathematical way of writing the square root of 841 which is equivalent to 29. As 29 is an integer and a rational number so 841 is a perfect square which in other words can be written as √841 is a rational number. This article explains how to find the square root of 841
In this article, we will analyze and find the square root of 841 using various mathematical techniques, such as the approximation method and the long division method.
What Is the Square Root Of 841?
The square root of the number 841 is 29.
The square root can be defined as the quantity that can be doubled to produce the square of that similar quantity. In simple words, it can be explained as:
√841 = √(29 x 29)
√841 = √(29)$^2$
√841 = ±29
The square can be canceled with the square root as it is equivalent to 1/2; therefore, obtaining 29. Hence 29 is 841’s square root. The square root generates both positive and negative integers.
How To Calculate the Square Root of 841?
You can calculate the square root of 841 using any of two vastly used techniques in mathematics; one is the Approximation technique, and the other is the Long Division method.
The symbol √ is interpreted as 841 raised to the power 1/2. So any number, when multiplied by itself, produces its square, and when the square root of any squared number is taken, it produces the actual number.
Let us discuss each of them to understand the concepts better.
Square Root by Long Division Method
The process of long division is one of the most common methods used to find the square roots of a given number. It is easy to comprehend and provides more reliable and accurate answers. The long division method reduces a multi-digit number to its equal parts.
Learning how to find the square root of a number is easy with the long division method. All you need are five primary operations- divide, multiply, subtract, bring down or raise, then repeat.
Following are the simple steps that must be followed to find the square root of 841 using the long division method:
Step 1
First, write the given number 841 in the division symbol, as shown in figure 1.
Step 2
Starting from the right side of the number, divide the number 841 into pairs such as 41 and 8.
Step 3
Now divide the digit 8 by a number, giving a number either 8 or less than 8. Therefore, in this case, the remainder is 4, whereas the quotient is 2.
Step 4
After this, bring down the next pair 41. Now the dividend is 441. To find the next divisor, we need to double our quotient obtained before. Doubling 2 gives 4; hence consider it as the next divisor.
Step 5
Now pair 4 with another number to make a new divisor that results in $\leq$ 441 when multiplied with the divisor.
Step 6
Adding 9 to the divisor and multiplying 49 with 9 results in m $\leq$ 441. The remainder obtained is 00.
Step 7
The resulting quotient 29 is the square root of 841. Figure 1 given below shows the long division process in detail:
Important points
- The number 841 is a perfect square.
- The number 841 is a rational number.
- The number 841 can be split into its prime factorization.
Is Square Root of 841 a Perfect Square?
The number 841 is a perfect square. A number is a perfect square if it splits into two equal parts or identical whole numbers. If a number is a perfect square, it is also rational.
A number expressed in p/q form is called a rational number. All the natural numbers are rational. A square root of a perfect square is a whole number; therefore, a perfect square is a rational number.
A number that is not a perfect square is irrational as it is a decimal number. As far as 841 is concerned, it is a perfect square. It can be proved as below:
Factorization of 841 results in 29 x 29 which can also be expressed as 29$^2$.
Taking the square root of the above expression gives:
= √(29$^2$)
= (29$^2$)$^{1/2}$
= 29
This shows that 841 is a perfect square and a rational number.
Therefore the above discussion proves that the square root of 841 is equivalent to 29.
Images/mathematical drawings are created with GeoGebra.