Square Root of 35

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

• Square Root of 35: √35 = 5.91607
• Square of 35: 35² = 1225

The square root of 35 is a number whose square gives the original number. By trial and error method, we can see that, there does not exist any integer whose square is 35.
The value of √35 is 5.91607978309961...
To check this answer, find (5.91607978309961)² and we can see that we get 34.999... which is very close to 35.

A rational number is a number which can either be:

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

In the previous section, we saw that: √35 = 5.91607978309961...
Clearly, this is non-terminating and the decimal part has no repeating pattern. So it is NOT a rational number. Thus, √35 is an irrational number.

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

1. Repeated Subtraction
2. Prime Factorization
3. Estimation and Approximation
4. Long 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.
• 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

If we repeat this process further, we get, √35 = 5.91607978309961...

Explore Square roots using illustrations and interactive examples

• Square Root of 34
• Square Root of 44
• Square Root of 27
• Square Root of 29
• Square Root of 5

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. 

Think Tank:

• Can the value of √35 be -5.91607978309961... as well? Hint: Think what is the value of (-5.91607978309961...)²
• Is √35 a real number? Hint: Think whether there is any real number whose square is negative.

What is the square root of 35 simplified?

√35 cannot be simplied. Hence, it remains same.

What is the square of 35?

The square of 35 is, 35² = 1156.

What is the approximate square root of 35?

As we learned in this page, √35 is 5.8309518948...

Is 35 square root a rational number?

As we have already learned on this page, the square root of 35 is NOT a rational number. It is an irrational number because its decimal value is 5.8309518948..., which is non-terminating and it has no repeated pattern in its decimal part.

Is the square root of 35 rational or irrational?

The square root of 35 is irrational.

Is square root of 35 a real number?

Yes, the square root of 35 is a real number.