The square of root 1156 is 34. The square root of a number is a number that, when multiplied two times to itself gives the perfect square number. The square root of 1156 is written as √1156, where ‘√’ is called the radical sign. The square root of 1156 in exponential form is written as (1156)½ . Since the square root of 1156 is a whole number, hence 1156 is a perfect square number. In this article, we shall learn how to find the square root of 1156
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Square Root of 1156 |
± 34 |
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Square of 1156 |
13,36,336 |
What is the Square Root of 1156?
The square root of 1156 is a number whose square is 1156. Now, if we square both 34 and –34 we get the answer 1156. Thus, the square root of 1156 is both 34 and –34, we choose the positive or the negative root as per the requirement of the problem.
We can also express the square root of 1156 as the roots of the quadratic equation x2 – 1156 = 0.
x2 – 1156 = 0
⇒ x2 = 1156 (taking square roots on both sides)
⇒ x = √(1156)
⇒ x = ± 34
Check out the properties of perfect square numbers.
How to Find the Square Root of 1156?
Let us calculate the square root of 1156 using different methods:
- Repeated subtraction method
- Prime factorisation method
- Long division method
Repeated Subtraction Method
Square of any perfect square number could be determined by the repeated subtraction method. In this method, we have to repeatedly subtract the given number by consecutive odd numbers until we get the answer zero. The nth odd number for which we get the answer zero is the square root of the given number.
Thus, we have 1156 – 1 = 1155, 1155 – 3 = 1152, 1152 – 5 = 1147, continuing in this way we get for the 34th odd number the answer is zero.
∴ 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 = 1156.
This method is quite a time-consuming method, and for larger numbers, this method is not preferable. Instead, we can use the prime factorisation method to calculate the square roots.
Prime Factorisation Method
We shall prime factorise the given then make pairs of two for each number to find the square root of the number.
Prime factorisation of 1156 = 2 × 2 × 17 × 17
√1156 = √(2 × 2 × 17 × 17) = 2 × 17 = 34.
Thus, to find the square root of any number by the prime factorisation method, the following are steps:
- Prime factorise the given number
- Make pairs of two for each of the prime factors.
- Take only one prime factor for each pair.
- If any prime remains unpaired, then the number is not a perfect square.
Long Division Method
To calculate the square root of 1156 by the long division method, we make pairs of digits of 1156 from right to left. Then perform the division as follows:
To learn how to find the square root of any number by the long division method, click here.
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Solved Examples on Square Root of 1156
Example 1:
Find the smallest number which must be multiplied to 578 to make it a perfect square number. Also, find the square root of the perfect square number.
Solution:
Prime factorisation of 578 = 2 × 17 × 17
We observe that only 2 remains unpaired. Thus 2 must be multiplied to 578.
578 × 2 = 1156 is the perfect square number.
Square root of 1156 = √[2 × 2 × 17 × 17] = 2 × 17 = 34.
Example 2:
There are 1156 chairs in an auditorium hall. If there are an equal number of rows and columns of chairs, find out how many rows are there in the hall.
Solution:
Let there be x numbers of rows and columns in the hall.
Total number of chairs in th hall = x × x = 1156
⇒ x2 = 1156
Taking square roots on both the sides, we get,
x = √1156 = 34
∴ there are 34 rows of chairs in the hall.
Example 3:
Find the diameter of the sphere whose total surface area is 14519.36 cm2. (Use 𝜋 = 3.14)
Solution:
Let r be the radius of the sphere.
The total surface area of the sphere = 4𝜋r2 = 14519.36 cm2
⇒ r2 = (14519.36)/( 4 × 3.14) = 1156
⇒ r = √1156 = 34 cm
∴ diameter of the sphere is 2 × 34 = 68 cm.
Frequently Asked Questions on Square Root of 1156
What is the square root 1156?
The square root of 1156 is 34.
Is 1156 a perfect square number?
Yes, 1156 is a perfect square number and 34 × 34 = 1156.
What is the prime factorisation of 1156?
The prime factorisation of 1156 is 2 × 2 × 17 × 17.
How many consecutive odd numbers must be added to get 1156?
The first 34 consecutive odd numbers must be added to get 1156. Thus, √1156 = 34.
How do you find the square root of 1156?
We can find find the square root of 1156 by the prime factorisation method. The prime factorisation of 1156 = 2 × 2 × 17 × 17. By making the pairs of two, the square root of 1156 = √[2 × 2 × 17 × 17] = 2 × 17 = 34.
