Square Root of 841

In Mathematics, the square root of 841 is defined as a number, which on multiplication by itself for two times, results in the original number 841. The value of the square root of 841 is a rational number since it can be represented in the form of p/q. In this article, we will learn two different such as the long division method and the prime factorization method to determine the square root of 841 with complete explanation.

Table of Contents:

• What is the Value of Square Root of 841?
• Radical Form of Square Root of 841
• Prime Factorization Method to Find √841
• Long Division Method to Find √841
• Examples
• FAQs

What is the Value of Square Root of 841?

If a number is multiplied by itself and gives the result as 841, then we can say that the number is the square root 841. Symbolically, the square root of 841 is expressed as √841.

Hence, √841 = √(Number × Number)

Hence, by multiplying the number 29 for two times, we get the original number 841.

(i.e) √841 = √(29× 29)

√841 = √(29)²

On removing square and square root, we will get

√841 = ± 29

Square Root of 841 in Radical Form

The simplest radical form of the square root of 841 is √841. Generally, the radical form of the square root of a number can be written, if we know the prime factorization of a number. Thus, the prime factorization of 841 is 29 × 29. Thus, if we write the square root of 841 in radical form (i.e) √29 × √29, it should not be the simplest radical form.

Square Root of 841 by Prime Factorization Method

The square root of 841 can be found using the prime factorization method. To find the value, we should know the prime factorization of 841. Thus, the prime factorization of a number 841 is 29 × 29.

Thus, √841 = √(29 × 29)

√841 = (√29)²

√841 = 29

Hence, the square root of 841 is equal to 29.

Square Root of 841 by Long Division Method

The steps to obtain the square root of 841 using the long division method is provided as follows:

Step 1: First, write the number 841. Next, Pair the number 841 by putting the bar on the top of the number from right to left.

Step 2: Next, divide a number 8 by a number, such that the multiplication of the same number must be less than or equal to 8. Hence, 2×2=4, which is smaller than 8. Thus, we get quotient = 2 and remainder = 4.

Step 3: Double the quotient value, therefore we get 4 and let us take 40 as the new divisor. Now, bring down the number 41 for the division process. Thus, the new dividend obtained is 441. Now, determine the number, such that (40 + new number) × new number will give the product that should be smaller than or equal to 441. Hence, (40+9) × 9 = 441, which is equal to 441.

Step 4: Subtract 441 from 441, and we get 00 as the new remainder, and 29 as a quotient.

Step 5: Thus, the value of the square root of 841, √841 is 29.

Video Lessons on Square Roots

Visualising square roots

Finding Square roots

Examples

Example 1:

Simplify the expression: (4√841)/2.

Solution:

Given: (4√841)/2.

As we know that the square root of 841 is 29.

Substituting the value in the expression,

(4√841)/2 = [4(29)]/2

(4√841)/2 = 2(29) = 58

Therefore, the simplification of (4√841)/2 is 58.

Example 2:

Compute the value of k, if k√841 + 20 = 107.

Solution:

Given: k√841 + 20 = 107 …(1)

We know that √841 = 29

Now, substitute the value in equation (1), we get

k(29) + 20 = 107

29k = 107 – 20

29k = 87

k = 87/29

k = 3.

Therefore, the value of k is 3

Example 3:

Simplify the expression: (2√841 × 5√841) + 40

Solution:

Given expression: (2√841 × 5√841) + 40

(2√841 × 5√841) + 40 = [10(√841)²] +40

On removing square and square root, we get

(2√841 × 5√841) + 40 = [10(841)] + 40

(2√841 × 5√841) + 40 = 8410 + 40

(2√841 × 5√841) + 40 = 8450.

Hence, the simplified form of (2√841 × 5√841) + 40 is 8450.