Square Root of 33
Do you know that between 5^{2 }and 6^{2}, we have 10 numbers. Between n^{2 }and (n+1)^{2}, we have 2n numbers. 33 lies between 5^{2 }and 6^{2}. In this minilesson let us learn to calculate the square root of 33 by long division and approximation methods.
 Square Root of 33: 5.744
 Square of 33: 33^{2} = 1089
What Is the Square Root of 33?
 The square root of 33 is 33 raised to the power ½. 33^{½ }= (number × number) ^{½} = √33
 5.744 × 5.744 = √33 and 5.744 × 5.744 = √33
 √33 = ± 5.744
Is Square Root of 33 Rational or Irrational?
The square root of 33 is an irrational number where the numbers after the decimal point go up to infinity. √33 = 5.744562646538029 which cannot be expressed as a rational number of the form p/q. Thus, the square root of 33 is an irrational number.
How to Find the Square Root of 33?
The square root of 33 or any number can be calculated using the approximation method and the long division method.
Square Root of 33 using the Approximation Method
 √25 < √33 < √36
 5 < √33 < 6
 Thus, we estimate the value of the square root of 33 to lie between 5 and 6.
 To approximate the value, divide 33 by 6. 33 ÷ 6 = 5.5
 To come closer to the accurate value, find the average between 5.5 and 6.
 We obtain the average as (5.5+6)/2 = 11.5/2 = 5.75
Square Root of 33 by the Long Division Method
The long division method helps us find a more accurate value of the square root of any number. Let's see how to find the square root of 33 by the long division method. Here are the steps to be followed:
 Write 33 as 33. 00 00 00
 Divide 33 by a number such that number × number gives 33 or a number less than that.
 We know 5 × 5 = 25. Subtract this from 33 and we get 8. Bring down a pair of zeros. 800 is the new dividend.
 Quotient is 5. Double the quotient. We get 10. Now we have 10x at the new divisor's place. Find a number in the place of x such that 10 x × x gives 800 or less than that.
 We find 107 × 7 is 749. Subtract it from 800 and get the remainder as 51. Bring down the next pair of zeros.
 Double the quotient. We obtain 114. Let us have 114x at the new divisor's place. Find a number in the place of x such that 114 x × x gives 5100 or less than that.
 We find 1144 × 4 is 4576. Subtract it from 5100 and get the remainder as 524
 Repeat the process by bringing down the zeros and by doubling the quotient.
 Thus √33 = 5.744 to the nearest thousandths.
Explore square roots using illustrations and interactive examples:
Tips and Tricks
 √33 lies between √25 and √36 on estimation. Clearly, √33 lies between the whole numbers 5 and 6.
 8 is subtracted from 33 (33  8 = 25), 3 should be added (33 + 3 = 36) and 33 should be multiplied (33 × 33 = 1089) or divided (33 ÷ 33 = 1) to make it a perfect square.
Important Notes
 The square root of 33 is 5.744 approximated to 3 decimal places.
 The simplified form of square root of 33 in its radical form is √33
 √33 is an irrational number.
Square Root of 33 Solved Examples

Example 1: There are 33 students participating in a parade. They need to stand in such a way that the number of rows is equal to the number of columns. How many students would be left out in this arrangement?
Solution:
33 = rows × columns
Required rows = columns
Let us assume rows = columns = n
33 = n × n
n^{2 }= 33
n = √33
On finding the square root, using the long division method, we find that 8 is the remainder.
Thus 8 is number to be subtracted from 33.
33  8 = 25
We know that 25 is a perfect square and √25 is 5.
The students are to stand in 5 rows and 5 columns. With this arrangement, 8 students would be left out.

Example 2: Evaluate the square root of (33/48)
Solution:
Square root of (33/48) = √33/ √48
√33 = √(3 × 11)
√48 = √(3 × 16) = 4√3
√33 /√48 = √(3 × 11)/ 4√3
√(33/48) = √(11) ÷ 4
FAQs on Square Root of 33
What is the square root of 33?
The square root of 33 is ± 5.744
How do you write the square root of 33 in its simplified form?
√33 is the simplest radical form.
33 is the square root of which number?
33 is the square root of 1089.
Is square root of 33 a rational number?
The square root of 33 is an irrational number, because the value of √33 is a nonterminating decimal. √33 = 5.744562646538029
How to find the square root of √33?
The accurate value of √33 can be found using the long division method.
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