Square Root of 34
The square root of 34 is a number whose square gives the original number (34). In this chapter, we will calculate the square root of 34 by long division method along with solved examples and interactive questions.
Let us see what the square root of 34 is.
 Square Root of 34: √34 = 5.83095
 Square of 34: 34^{2} = 1156
1.  What Is the Square Root of 34? 
2.  Is Square Root of 34 Rational or Irrational? 
3.  How to Find the Square Root of 34? 
4.  Important Notes 
5.  Thinking Out of the Box! 
6.  FAQs on Square Root of 34 
What Is the Square Root of 34?
By trial and error method, we can see that there does not exist any integer whose square is 34. But we can find the square root of 34 using a calculator as √34 = 5.830951894845300... To check this answer, find (5.830951894845300)^{2} and we can see that we get 33.999... which is very close to 34.
Is the Square Root of 34 Rational or Irrational?
A rational number is a number which is:
 either terminating
 or nonterminating and has a repeating pattern in its decimal part
In the previous section, we saw that: √34 =5.830951894845300...
Clearly, this is nonterminating and the decimal part has no repeating pattern. So it is not a rational number.
Thus, √34 is an irrational number.
How to Find the Square Root of 34?
We can find the square root of 34 using various methods.
 Repeated Subtraction
 Prime Factorization
 Estimation and Approximation
 Long Division
If you want to learn more about each of these methods, click here.
Simplified Radical Form of Square Root of 34
The prime factorization of 34 is 34 = 2 × 17
To find the square root of any number, we take one number from each pair consisting of same numbers and we multiply them. But the prime factorization of 34 is 2 × 17, which has no pairs consisting of same numbers. Thus, √34 cannot be simplified any further.
Square Root of 34 by Long Division Method
The square root of 34 can be found using the long division as follows.
The long division process of finding the square root is not the same as the normal long division.
 Step 1: In this step, we take 34 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 34 and less than or equal to 34. We know that 5^{2} = 25. 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 34 to carry forward, we write pairs of zeros after the decimal point (as 34 = 34.000000...). We write as many pairs as we want the number of decimals after the decimal point in the final result. Let us calculate √34 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. So 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 900 and is less than or equal to 900. We have 108 × 8 = 864. Thus, the required number is 8. 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 √34 = 5.830
If we repeat this process further, we get, √34 = 5.830951894845300...
Explore Square roots using illustrations and interactive examples
Important Notes:
 34 lies between 25 and 36. So √34 lies between √25 and √36.That is, √34 lies between 5 and 6.
 The prime factorization method is used to write a square root of a nonperfect square number in the simplest radical form. For example: 45 = 3 × 3 × 5 = 3^{2} × 3^{5}. So, √45 = √3^{2} × √5 = 3√5.
Think Tank:
 Can the value of a square root be negative as well? Hint: Think what is the square of a negative number.
 Is √34 a real number?Hint: Think whether there is any real number whose square is negative.
Square Root of 34 Solved Examples

Example 1: Harper wants to cover her bathroom floor with tiles. The floor is squareshaped and it has an area of 34 square feet. What is the length of her bathroom?
Solution
Let us assume that the length of the bathroom is x feet. Then the area of the bathroom's floor is x^{2} square feet.
By the given information:
x^{2 }= 34
x = √34 = 5.83 feet 
Example 2: Patrick prepared a pizza of area 34π square inches. Find its radius. Round the answer to the nearest integer.
Solution
Let us assume that the radius of the pizza is r inches. Then its area using the formula of area of a circle is πr^{2} square inches. By the given information, πr^{2} = 34π
r^{2} = 34
By taking the square root on both sides, √r^{2} = √34. We know that the square root of r^{2 }is r. By calculating the square root of 34 and rounding the answer to the nearest integer,
Hence, the radius of pizza = 5.83 inches
FAQs On Square Root of 34
What is the square root of 34 simplified?
As we learned on this page, √34 is approximately 5.8309518948...
What is the square of 34?
The square of 34 is 34^{2} = 1156
What is the approximate square root of 34?
As we learned in this page, √34 is approximately 5.8309518948...
Is the square root of 34 a rational number?
As we have already learned in this page, the square root of 34 is NOT a rational number. It is an irrational number because its decimal value is 5.8309518948..., which is nonterminating and it has no repeated pattern in its decimal part.
Is square root of 34 a real number?
Yes, the square root of 34 is a real number.