Square root of 34
2026-02-28 13:10 Diff
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Last updated on August 5, 2025

The square root of 34 is the inverse operation of squaring a value “y” such that when “y” is multiplied by itself → y ⤫ y, the result is 34. It contains both positive and a negative root, where the positive root is called the principal square root.

What Is the Square Root of 34?

The square root of 34 is ±5.83095. The positive value, 5.83095 is the solution of the equation x2 = 34.


As defined, the square root is just the inverse of squaring a number, so, squaring 5.83095 will result in 34.  The square root of 34 is expressed as √34 in radical form, where the ‘√’  sign is called the “radical”  sign. In exponential form, it is written as (34)1/2 

Finding the Square Root of 34

We can find the square root of 34 through various methods. They are:

  • Prime factorization method
  • Approximation/Estimation method

Square Root of 34 By Prime Factorization Method

The prime factorization of 34 involves breaking down a number into its factors. Divide 34 by prime numbers, and continue to divide the quotients until they can’t be separated anymore.

After factoring 34, make pairs out of the factors to get the square root. If there exists numbers which cannot be made pairs further, we place those numbers with a “radical” sign along with the obtained pairs

So, Prime factorization of 34 = 2 × 17   


for 34, no pairs of factors can be obtained, but a single 17 and a single 2 are obtained.


So, it can be expressed as  √34 = √(17  × 2) = √34


√34 is the simplest radical form of √34

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Square Root of 34 by Long Division Method

This is a method used for obtaining the square root for non-perfect squares, mainly. It usually involves the division of the dividend by the divisor, getting a quotient and a remainder too sometimes.

Follow the steps to calculate the square root of 34:


Step 1 : Write the number 34, and draw a bar above the pair of digits from right to left.

                Step 2 : Now, find the greatest number whose square is less than or equal to 34. Here, it is 5, Because 52=25 < 34

Step 3 : Now divide 34 by 5 (the number we got from Step 2) such that we get 5 as quotient, and we get a remainder. Double the divisor 5, we get 10 and then the largest possible number A1=8 is chosen such that when 8 is written beside the new divisor, 10, a 3-digit number is formed →108 and multiplying 8 with 108 gives 864 which is less than 900.

Repeat the process until you reach remainder 0.


We are left with the remainder, 11100 (refer to the picture), after some iterations and keeping the division till here, at this point 

              Step 4 : The quotient obtained is the square root. In this case, it is 5.830…

Square Root of 34 by Approximation Method

Approximation or estimation of square root is not the exact square root, but it is an estimate.


Here, through this method, an approximate value of square root is found by guessing.

Follow the steps below:


Step 1 : Identify the square roots of the perfect squares above and below 34.


Below : 36→ square root of 36 = 6     ……..(i)


 Above : 49 →square root of 49 = 7     ……..(ii)


Step 2 : Divide 34 with one of 6 or 7 


 If we choose 6, and divide 34 by 6, we get 5.666   …….(iii)

              Step 3: Find the average of 6 (from (i)) and 5.6666 (from (iii))


 (6+5.6666)/2 = 5.8333


Hence, 5.8333 is the approximate square root of 34

Common Mistakes and How to Avoid Them in the Square Root of 34

When we find the square root of 34, we often make some key mistakes, especially when we solve problems related to that. So, let’s see some common mistakes and their solutions.
 

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Problem 1

Simplify √34 + 2√34 ?

Okay, lets begin

√34 + 2√34

= √34(1+2)

= 3√34


Answer :   3√34
 

Explanation

The simplest radical form of √34 is √34, so, it is taken common outside and calculated simply.

Well explained 👍

Problem 2

What is √34 multiplied by 2√34?

Okay, lets begin

 √34 ⤬ 2√34

= 34⤬2

= 68


Answer: 68 
 

Explanation

√34  multiplying with itself gives 34, and then again multiplied by 2. 
 

Well explained 👍

Problem 3

Find the value of 1/√34?

Okay, lets begin

1/√34

= 1/ 5.83095

=0.171


Answer: 0.171
 

Explanation

we divide 1 by the value of √34.
 

Well explained 👍

Problem 4

If y=√34, find y^2

Okay, lets begin

 firstly, y=√34= 5.83095


Now, squaring y, we get, 


 y2= (5.83095)2=34


or, y2 = 34


Answer : 34
 

Explanation

 squaring “y” which is same as squaring the value of √34 resulted to 34.

Well explained 👍

Problem 5

Find √34 / √34

Okay, lets begin

 √34/√34

= √(34/34)

= √1

= 1


Answer : 1 
 

Explanation

since the numerator and denominator is same, the answer is 1
 

Well explained 👍

FAQs on 34 Square Root

1.What is the √34 in fraction?

The √34 cannot be written in fractional form since the value is an irrational number.

2.What is the square of 34 ?

1156 is the square of 34. 
 

3.Is 34 a perfect square or non-perfect square?

34 is a non-perfect square, since 34 =(5.83095)2.
 

4.Is the square root of 34 a rational or irrational number?

The square root of 34 is ±5.83095. So, 5.83095 is an irrational number, since it cannot be obtained by dividing two integers and cannot be written in the form p/q, where p and q are integers.
 

5. What is the cube root of 34?

cube root of 34 is 3.2396

Important Glossaries for Square Root of 34

  • Exponential form: An algebraic expression that includes an exponent. It is a way of expressing the numbers raised to some power of their factors. It includes continuous multiplication involving base and exponent. Ex: 3 ⤬ 3 ⤬ 3 ⤬ 3 = 81 Or, 3 4 = 81, where 3 is the base, 4 is the exponent 
  • Factorization : Expressing the given expression as a product of its factors. Ex: 52=2 ⤬ 2 ⤬ 13 
  • Prime Numbers: Numbers which are greater than 1, having only 2 factors as →1 and Itself. Ex: 1,3,5,7,....
  • Rational numbers and Irrational numbers: The Number which can be expressed as p/q, where p and q are integers and q not equal to 0 are called Rational numbers. Numbers which cannot be expressed as p/q, where p and q are integers and q not equal to 0 are called Irrational numbers. 
  • perfect and non-perfect square numbers: Perfect square numbers are those numbers whose square roots do not include decimal places. Ex: 4,9,25 Non-perfect square numbers are those numbers whose square roots comprise decimal places. Ex :2, 8, 18

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Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.