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Let us see what the square root of 35 is:
|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?|
|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.
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.