Square root of 21
The total number of dots or the sum of all the numbers on a 6sided die? Yes – it is a total of 21! Square root of a number is obtained by raising the number to the power half. This chapter will cover finding the square root of 21 by division method and the average method.
 Square Root of 21: 4.582
 Square of 21: 441
1.  What Is the Square Root of 21? 
2.  Is Square Root of 21 Rational or Irrational? 
3.  How to Find the Square Root of 21? 
4.  FAQs on Square Root of 21 
What Is the Square Root of 21?
 The square root of a number is the number that gets multiplied to itself to give the original number.
 √21= 4.582 × 4.582
 √21 = (21)^{½} in its exponential form and √21 in its simplest radical form.
Is the Square Root of 21 Rational or Irrational?
 A number is said to be irrational if it cannot be expressed in the form of a ratio p/q, where q not equal to 0.
 √21 = 4.58257569495584 which is a non terminating decimal. Thus √21 is irrational.
How to Find the Square Root of 21?
The square root of a number can be calculated using different methods:
 Long Division method
 Average method
√21 cannot be simplified any further. So we can just express it as √(7 × 3). Hence we cannot use the prime factorization method to determine the square root of 21.
Square Root of 21 by Long Division Method
 Step 1: Write 21 as 21.000000. Now take the numbers as pairs from the right. In the left we have 21.Find a number that multiplied by itself gives 21 or less than that.
 Step 2: 4 × 4 = 16. Subtract 16 from 21. Get the remainder as 5 and bring one pair of zeros. Now the new dividend is 500.
 Step 3: Multiply the quotient 4 by 2. We get 8. Have 80 as the new divisor. Choose a number that added with 80 and multiplied by the sum obtained is 500 or less than that.
 Step 4: We find 5 added to 80 is 85 and 85 × 5 = 425. Subtract 425 from 500 and get the remainder as 75. Bring down the next pair of zeros. 7500 is the new dividend.
 Step 5: Multiply the quotient 45 by 2. We get 90. Have 900 as the new divisor. Choose a number that added with 900 and multiplied by the sum so obtained is 7500 or less than that.
 Step 6: We find 8 + 900 is 908 and 908 × 8 = 7264. Subtract 7264 from 7500 and get the remainder as 236. Bring down the next pair of zeros. 23600 is the new dividend.
 Repeat the division process till we get the remainder.
 Thus we have accurately determined the value of square root of 21 as 4.582.
Square Root of 21 by Average Method
 The value of √21 lies between √16 and √25
 √16 < √21 < √25
 4 < √21 < 5
 Divide 21 by 5. We get 21 ÷ 5 = 4.25
 Now find the average of the quotient and the divisor in the previous step.
 ( 4.25 + 5 ) ÷ 2 = 9.25 ÷ 2 = 4.625
 √21 ≈ 4.625
 Thus √21 lies between the two perfect squares, 4 and 5.
Explore square roots using illustrations and interactive examples
Important Notes:
 √21 = 4.582 approximated to 3 decimal places.
 √21 is irrational as it is not a perfect square.
 Use average method to find the approximate value of √21 and division method to find the accurate value of √21
Square Root of 21 Solved Examples

Example 1: Evaluate √21 + √28
Solution: √21 = √(7 × 3)
√28 = √(7 × 4)
√21 + √28 = √(7 × 3) + √(7 × 4)
= √7 (3 + 4)
= √7 (7) = 7√7
√21 + √28 = 7√7

Example 2 : Evaluate 3√12 ÷ 2√21
Solution:
3√12 = 3√(3 × 4) = 6√3
2√21 = 2 √(7 × 3) = 2 √7√3
3√12 ÷ 2√21 = 6√3 ÷ 2 √7√3
= 3√7

Example 3 : A square flower garden has an area of 21 square units. What is the length of one side of the garden?
Area = side × side sq units
Side^{2} = 21
Side = √21
Side = 4.582 units
FAQs on Square Root of 21
What is the square root of 21?
Thus, the square root of 21 is 4.58257569495584.
Is the square root of 21 negative 4.58257569495584?
The square root of 21 means the number which when multiplied with itself gives the product as 21.
√21 = √( 4.58257569495584 × 4.58257569495584) and also = √( 4.58257569495584 ×  4.58257569495584)
Thus, negative 4.58257569495584 is also a square root of 21.
Is √21 an irrational number?
An irrational number is a number that cannot be represented in the simple form of a fraction.
√21 is 4.58257569495584. Thus √21 is an irrational number.
What are the methods to find the square root of 21?
We can find the square root of 21 using long division method or average method.