The square root of 841 is a number that, when multiplied by itself, yields the original number 841. The square root of 841 is a rational number, as it can be expressed as a fraction. In this article, we will explore two different methods to find the square root of 841: the long division method and the prime factorization method.
Table of Contents:
The square root of 841 is the number that yields 841 when multiplied by itself. We denote the square root of 841 as √841.
So, √841 = √(Number × Number)
By multiplying the number 29 twice, we get the original number 841.
Thus, √841 = √(29× 29)
So, √841 = √(29) 2
Removing the square and the square root, we get √841 = ± 29
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Square Root of 841: 29. |
The simplest radical form of the square root of 841 is √841. The radical form of the square root of a number can be written if we know the prime factorization of the number. The prime factorization of 841 is 29 × 29. So, the square root of 841 in radical form is not √29 × √29.
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Square Root of 841 in Radical Form: √841. |
The steps to find the square root of 841 using the long division method are as follows:
Step 1 : Write the number 841. Pair the number 841 by putting a bar over the number from right to left.
Step 2 : Divide the number 8 by a number so that the multiplication of the same number is less than or equal to 8. So, 2×2=4, which is less than 8. We get a quotient of 2 and a remainder of 4.
Step 3 : Double the quotient to get 4, and take 40 as the new divisor. Bring down the number 41 for the division process, to get a new dividend of 441. Find a number such that (40 + new number) × new number gives a product that is less than or equal to 441. So, (40+9) × 9 = 441, which equals 441.
Step 4 : Subtract 441 from 441 to get a new remainder of 00, and a quotient of 29.
Step 5 : Therefore, the square root of 841, √841, is 29.
Example 1:
Simplify the expression: (6√841)/3.
Solution:
Given: (6√841)/3.
As we know that the square root of 841 is 29.
Substituting the value in the expression,
(6√841)/3 = [6(29)]/3
(6√841)/3 = 2(29) = 58
Therefore, the simplification of (6√841)/3 is 58.
Example 2:
Find the value of k, if k√841 + 10 = 49.
Solution:
Given: k√841 + 10 = 49 …(1)
We know that √841 = 29
Now, substitute the value in equation (1), we get
k(29) + 10 = 49
29k = 49 – 10
29k = 39
k = 39/29
k = 1.34 (approx).
Therefore, the value of k is 1.34 (approx)
What is the value of the square root of 841?
The value of √841 is equal to 29.
How to express the square root of 841 in radical form?
The square root of 841 in radical form is expressed as √841.
Is 841 a perfect square?
Yes, 841 is a perfect square, since it is expressed as the product of two equal integers. (i.e) 841 = 29×29.
Compute the value of the square of square root of 841.
The value of the square of square root of 841 is 841.
What is 29 plus the square root of 841?
We know that √841 is 29. Hence, 29+29 = 58.