In mathematics, the square root of 21 is defined as a number that produces the original number 21, when multiplied by itself twice. The square root of 21 is an irrational number since it cannot be stated in the form p/q. In this article, we will go through two different ways to find the square root of 21, including the long division method and the prime factorization method with detailed explanations.
What is the Square Root of 21?
When a number is multiplied by itself and the result is 21, the number is said to be the square root of 21. The square root of 21 is represented symbolically by √21.
As a result, √21 = √(Number × Number)
Thus, multiplying the number 4.582 twice generates the original number 21.
(i.e.) √21 = √(4.582 × 4.582)
√21 = √(4.582)2
When we remove the square and square root, we obtain
√21 = ±4.582
|
Square Root of 21 in Decimal Form: 4.582 |
Square Root of 21 by Prime Factorization Method
The prime factorization method can be used to find the square root of 21. We’ll need to identify the prime factorization of 21 to figure out the answer. As a result, the prime factorization of 21 is 7 × 3.
Thus, √21 = √(7 × 3)
√21 = √7 × √3
As we know √7 = 2.646 and √3 = 1.732
Substituting the values, we get
√21 = 2.646×1.732
√21 = 4.582
As a result, the square root of 21 is approximately 4.582.
Square Root of 21 by the Long Division Method
Step 1: Write 21 in decimal form as 21.000000. Take the numbers from the right in pairs. We have 21 on the left. Find a number that, when multiplied by itself, equals 21 or less.
Step 2: So, 16 = 4 × 4. Subtract 16 from 21. Hence, the remainder is 5 and bring one pair of zeros. So, the new dividend is 500.
Step 3: Multiply the quotient by two and we get 8. Make the new divisor 80. Choose a number that, when added to 80 and multiplied by the result, is 500 or less.
Step 4: We find that adding 5 to 80 becomes 85, and 85×5 = 425. Subtract 425 from 500 and we have 75 as the remainder. Bring the next two zeros down. So, the new dividend is 7500.
Step 5: Multiply 45 by 2. We get the number 90. Make the new divisor 900. Choose a number that, when added to 900 and multiplied by the sum, equals or is less than 7500.
Step 6: We observe that 8 Plus 900 equals 908 and that 908×8 = 7264. Subtract 7264 from 7500 to obtain 236 as the remaining. Bring the next two zeros down. The new dividend is 23600.
Step 7: Repeat the dividing operation until we get the approximate value of the square root of 21.
Step 8: As a result, the value of the square root of 21 has been found to be 4.582.
| More on Square Root of a Number: |
Video Lessons on Square Roots
Visualising square roots
Finding Square roots
Examples
Example 1:
Simplify the expression: (10√21)/4.
Solution:
Given: (10√21)/4
As we know that the square root of 21 is 4.582.
Substituting the value in the expression,
(10√21)/4 = [10(4.582)]/4
(10√21)/4 = 45.82/4 = 11.455
Hence, the simplification of (10√21)/4 is 11.455.
Example 2:
Find the value of a, if a√21=60.
Solution:
Given: a√21=60. …(1)
We know that √21 = 4.582
Now, substitute the value in equation (1), we get
a(4.582) = 60
a = 60/4.582 = 13.094
Thus, the value of a is 13.094.
Example 3:
Simplify the expression: (7√21 × 2√21) + 10
Solution:
Given expression: (7√21 × 2√21) + 10
(7√21 × 2√21) + 10 = [14(√21)2] +10
On removing square and square root, we get
(7√21 × 2√21) + 10 = [14(21)] + 10
(7√21 × 2√21) + 10 = 294+10
(7√21 × 2√21) + 10 = 304.
Hence, (7√21 × 2√21) + 10 is 304.
To learn more square root of numbers and other Maths articles, stay tuned to BYJU’S – The Learning App, and download the app to watch many engaging videos.
Frequently Asked Questions on the Square Root of 21
What does the square root of 21 equal?
The value of the number √21 equals 4.582.
What is the radical form of the square root of 21?
In radical form, the square root of 21 is given as √21.
Is the number 21 a perfect square?
No, since it cannot be written as the product of two equal integers, 21 is not a perfect square.
Calculate the square of square root 21.
The square of the square root of 21 has a value of 21.
(i.e., (√21)2 = 21).
What is the sum of 10 and the square root of 21?
We already know that √21 equals 4.582.
As a result, 10+4.582 Equals 14.582.
Comments