Square Root of 33

Do you know that between 5² and 6², we have 10 numbers. Between n² and (n+1)², we have 2n numbers. 33 lies between 5² and 6². In this mini-lesson 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: 33² = 1089

• 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

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.

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:

• Square root of 36
• Square root of 54
• Square root of 16
• Square root of 26
• Square root of 60

• √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.

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 non-terminating 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.