Do you know how to find square root of 35? Stay tuned and learn with us how to calculate the square root of 35 by long division method along with solved examples and interactive questions.

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Let us see what the square root of 35 is:

Square Root of 35: √35 = 5.91607Square of 35: 352 = 1225
1.What Is the Square Root of 35?
2.Is Square Root of 35 Rational or Irrational?
3.How to Find the Square Root of 35?
4.Important Notes
5.FAQs on Square Root of 35
6.Thinking Out of the Box!


A rational number is a number which can either be:

either terminatingor non-terminating and has a repeating pattern in its decimal part.

It is possible to find the square root of 35 using various methods.

Repeated SubtractionPrime FactorizationEstimation and ApproximationLong Division

If you want to learn more about each of these methods, click here.

Simplified Radical Form of Square Root of 35

To find the square root of any number, we take one number from each pair of the same numbers from its prime factorization and we multiply them. But the prime factorization of 35 is 5 × 7 which has no pairs of the same numbers. Thus, 35 cannot be simplified any further and hence the simplest radical form of 35 is 35 itself.

Square Root of 35 by Long Division Method

The square root of 35 can be found using the long division as follows.

Step 1: In this step, we take 35 as a pair (by placing a bar over it). (If the number has an odd number of digits, then we place a bar just on the first digit; if the number has an even number of digits, then we place a bar on the first two digits together).Step 2: Find a number whose square is very close to 35 and less than or equal to 35. We know that 52=35. So 5 is such a number. We write it in the place of both the quotient and the divisor.Step 3: Since we do not have any other digits of 35 to carry forward, we write pairs of zeros after the decimal point (as 35 = 35.000000...). We write as many pairs as we want the number of decimals after the decimal point in the final result. Let us calculate 35 up to 3 decimals. So, we write 3 pairs of zeros. Since we have taken a decimal point in the dividend, let us write a decimal point in the quotient as well after 5.Step 4: Remember that we always carry forward two digits at a time while finding a square root. We carry forward two zeros at a time. Double the quotient and write it as the divisor of the next division. But, note that this is not the complete divisor.Step 5: Now a part of the divisor is 10, think which number should replace each of the boxes such that the product is very close to 1000 and that is less than or equal to 1000. We have 109 × 9 = 981. Thus, the required number is 9. Include it in both the divisor and quotient.

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Step 6: We repeat step 3 and step 4 for the corresponding divisors and quotients of the subsequent divisions.

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So far we have got 35 = 5.916

Explore Square roots using illustrations and interactive examples

Important Notes:

35 lies between 25 and 36. Among these, 35 is very close to and less than 36. So 35 is very close to and less than 36 = 6.The prime factorization method is used to find the square root of a perfect square number. For example: 36 = 2 × 2 × 3 × 3 = 22 × 32 . So, 36 = 22 × 32 = 2 × 3 = 6. 

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