Square Root of 1156
Squaring and finding the square root are inverse operations. When 1156 = a number × a number, then √1156 = a number. In this lesson, we will calculate the square root of 1156 by repeated subtraction method and prime factorization method and solve a few interesting problems.
 Square Root of 1156: √1156 = 34
 Square of 1156: 1156² = 13,36,336
What Is the Square Root of 1156?
 The square root of a number is the number that when multiplied to itself gives the original number as the product. Finding the square root of a number is the inverse process of squaring a number.
 1156 = a × a = a^{2 }
 Thus, a = √1156= √(34 × 34)
 34 ×34 = 1156 or 34 × 34 = 1156. Therefore √1156= ± 34
 This shows that 1156 is a perfect square.
Is the Square Root of 1156 Rational or Irrational?
 A rational number is defined as a number that can be expressed in the form of a quotient or division of two integers, i.e. p/q, where q is not equal to 0.
 1156 can be expressed as 34/1 and 34/1
 Both the numbers can be represented in the form of a rational number.
 Hence, the square root of 1156 is a rational number.
How to Find the Square Root of 1156?
The square root of 1156 can be calculated using different methods such as prime factorization or the repeated subtraction method.
Square Root of 1156 by Repeated Subtraction Method
 The sum of n consecutive odd numbers = n^{2 }. 1156 is the sum of first 34 odd natural numbers. 34^{2} = 1156
 1 + 3+ 5+ 7+ 9 + 11+ 13 + 15 + 17 + 19 + 21 + 23+ 25 + 27 + 29 + 31+ 33+ 35 + 37 + 39 + 41 + 43 + 45 + 47 + 49 + 51 + 53 + 55 + 57 + 59 + 61 + 63 + 65 + 67 = 34^{2 } = 1156
 Start from 1156 and keep subtracting the successive odd numbers till we obtain zero. The number of times we subtract is the square root of 1156.
 Therefore starting from 1156, we subtract 34 times to obtain 0. Thus, the square root of 1156 is 34.
Square Root of 1156 by Prime factorization method
 Prime factorization is expressing the number as a product of its prime factors.
 The prime factor of 1156 is 3. 1156 = 2 × 2 × 17 × 17
 The square root of 1156 is √1156 = √( 2 × 2 × 17 × 17)
 √1156 = √( 2^{2} × 17^{2}) ⇒ (1156^{½ })^{ }= ( 2^{ ½} × 17^{½} )
 Squaring on both the sides, (1156^{½ })^{2 }= ( 2^{ ½} × 17^{½} )^{2}
 We get 1156^{½} = 2 × 17 = 34
Explore Square roots using illustrations and interactive examples
Important Notes
 The square root of is expressed as √1156 in the radical form and as 1156 ^{½} in the exponential form.
 The square root of means the second root of 1156 = +34 or 34
 The square root of only perfect squares can be calculated easily using the prime factorization method or repeated subtraction method. 1156 is a perfect square.
Challenging Questions
 Can √1156 , √84100 and √82944 form a pythagorean triplet?
 What should be the least number multiplied to 1156 to make it a perfect cube?
Square Root of Solved Examples

Example 1: How can we divide 1156 using the division method?
Solution:
Write 1156 as 11 56 in pairs. 11 is the dividend now.
Find a (number x number) that gives ≤ 11. We find 3 × 3 = 9. subtract 9 from 11 and obtain 2 as the remainder.
Bring down the next pair of 56. 2 56 is our new dividend.
Double the quotient. It is 6. Now 60 is written in the new divisor's place.
Find a (number + 60) × number that gives the result ≤ 2 56. We determine that (60 + 4) × 4 = 256.
Subtract this from 256. We have completely divided 1156 as we have obtained the remainder as 0.
Thus, √1156 = 34

Example 2 : James has to buy a new carpet for the prayer hall. In the store, he finds a square carpet of area 1156 sq feet. How long is each side of the carpet? How many such carpets does he need to cover the hall of area 272 sq feet?
Solution:
Area of the square carpet = 1156 sq feet
The side of the carpet = √Area = √1156
Side = 34 feet
Number of carpets needed = 272 ÷ 34 = 8
FAQs on Square Root of 1156
What is the square root of 1156?
The square root of is ± 34
Is 1156 a perfect square?
The numbers ending with 0, 1, 4, 5, 6, or 9 at the units place are perfect squares. 1156 has the roots 34, which is a whole number. Thus 1156 is a perfect square.
Is the square root of 1156 an irrational number?
No, the square root of 1156 is a rational number. Since √1156 = ± 34 is a whole number, we can express it as the ratio of 34/1 and 34/1.
What is the square root of 1156 by prime factorization method?
1156 = 2 × 2 × 17 × 17 and √1156 = √(2 × 2 × 17 × 17 ) ⇒ √1156 = 2 × 17 = 34
What are the methods to find the square root of 1156?
We can find the square root of using prime factorization method, or repeated subtraction method.