Square Root of 22

The square root of 22 is expressed as √22 in the radical form and as (22)^½ or (22)^0.5 in the exponent form. The square root of 22 rounded up to 5 decimal places is 4.69042. It is the positive solution of the equation x² = 22.

• Square Root of 22: 4.69041575982343
• Square Root of 22 in exponential form: (22)^½ or (22)^0.5
• Square Root of 22 in radical form: √22

The value of the square root of 22 is 4.69041575982343.This the reason why 22 is called a non-perfect square. A perfect square is expressed as the product of an integer by itself.

Square Root of 22 in Radical Form

Expressing the number inside the radical sign √ is the square root of 22 in the radical form. The square root of 22 is already in the lowest form. 22 can be factored as 2 × 11. Therefore, the square root of 22 in radical form is √22

The square root of 22 is NOT a rational number. There is no integer which when multiplied by itself gives 22. Thus, it is not a perfect square. A number is a rational number if it is the quotient of two integers. However, √22 = 4.6904157982343, which shows that it is a non-terminating decimal. Thus, √22 is an irrational number.

We can find the square root of 22 by the following two methods:

• Approximation Method
• Long Division Method

Square Root of 22 by Approximation

We can find the square root of 22 by the method of approximation. Identify the two perfect squares between which 22 lies. 22 lies between 16 and 25. So, the square root of 22 lies between the square root of 16 (lower perfect square) and the square root of 25 (higher perfect square). We know that √16= 4 and √25 = 5. Therefore, the whole number part is 4. To find the decimal part, we use the following formula.
Irrational number- Lower perfect square / Bigger perfect square-Lower perfect square 
= (22-16) / (25-16)
= 6 / 9
=0.6
The whole number part + the decimal part = 4 + 0.6 (approx) 4.6

Square Root of 22 by Long Division Method

To find the square root of 22 by long division,

• Step 1:Write the pair of digits starting from one's place.  Here 22 is the pair to be taken. 
• Step 2: Find a divisor 'n' such that n × n results in a product that is less than or equal to 22. We know that 4 × 4 = 16
• Step 3: Find the difference as done in the usual division. (22-16= 6). Double the quotient that was calculated.4 × 2 and write it in the new divisor's place. Here it's 8. We leave a blank to create a new divisor.
• Step 4: Here we have no other numbers to divide. So, we keep a decimal point after the dividend 22 and quotient 4. Now, place 2 pairs of zeros after the decimal of the dividend. Bring the pair of zeros down.
• Step 5: Find a divisor 'n' such that n × n results in a product that is less than or equal to 600. Write the next quotient as 6. Now we get our new divisor as 86, as 6 × 86 = 516. Do the division and get the remainder. Here we get 84
• Step 6: Bring the next pair of zeros down.
• Step 7: Double the quotient 46. (2 × 46 = 92). Write it in the new divisor's place and leave a blank next to it.
• Step 8: Find a divisor 'n' such that n × n results in a product that is less than or equal to 8400. We find that 9 × 929= 8361. We can stop here as we have found the quotient up to 2 decimal places.

Thus, √22 = 4.69 by long division. We might proceed further to get the answer to further decimal places.

Explore Square roots using illustrations and interactive examples

• Square Root of 25
• Square Root of 24
• Square Root of 28
• Square Root of 225
• Square Root of 45

• We can find the actual value of √22= 4.69041575982343 by the long division method. 
• The square root of 22 is already in its simplest radical form and cannot be simplified.

• What is the value of √√22?
• Can you think of any quadratic equation which has a root as √22?