Square Root of 112
Timothy loves building square shapes with different materials. He plans on building one square with an area of 112 cm². To do this, he needs to know the side length of the square which he can get only by calculating the square root of 112. In this lesson, we shall learn how to calculate the square root of 112 and a few more facts.
Square Root of 112: √112 = 10.58300524...
Square of 112: 112^{2} = 12544
1.  What Is the Square Root of 112? 
2.  Is Square Root of 112 Rational or Irrational? 
3.  How to Find the Square Root of 112? 
4.  FAQs on Square Root of 112 
What Is the Square Root of 112?
The square root of a number n is written as √n. This number when squared or multiplied by itself results in the original number n. The square root of 112 can be written in multiple ways.
 Radical form: √112 = 4√7
 Decimal form: 10.583
 Exponent form: (112)^{1/2}
Is Square Root of 112 Rational or Irrational?
 112 is a number that is not a perfect square, meaning it does not have a natural number as its square root.
 Also, its square root cannot be expressed as a fraction of the form p/q which tells us that the square root of 112 is an irrational number.
How to Find the Square Root of 112?
There are multiple ways to find the square root of 112:
 Long Division Method
 Prime Factorization Method
One can find out more about these methods by clicking here.
Long Division Method
The square root of 112 by long division method consists of the following steps:
 Step 1: Starting from the right, we will pair up the digits of 112 by putting a bar above 12 and 1 separately. We also pair the 0s in decimals in pairs of 2 from left to right.
 Step 2: Find a number which, when multiplied by itself, gives a product less than or equal to 1. This will be 1 here, so place 1 in the quotient and in the divisor's place which will result in the remainder being 0.
 Step 3: Drag down 12 beside the remainder 0. Also, add the divisor to itself and write it below. (1+1=2)
 Step 3: Find a number X such that 2X × X results in a number less than or equal to 12. The number 0 fits here so fill it next to 2 in the divisor as well as next to 1 in the quotient.
 Step 4: Find the remainder and now drag down the pair of 0s from the decimal part of the number. Adding X to the divisor, the new divisor remains 20.
 Step 5: Repeat this process to get the decimal places you want.
Therefore, the square root of 112 = 10.583
Prime Factorization
 To find the square root of 112, we shall first express it in terms of its prime factors.
112 = 2 × 2 × 2 × 2 × 7  Next, this can be reduced further to
112 = 2^{4} × 7  Finally, to find the root of this from here is very easy,
√112 = √(2^{4} × 7)
√112 = 4√7 = 10.583
Therefore, the square root of 112 = 10.583
Explore square roots using illustrations and interactive examples
Important Notes
 There exists a positive and negative root of 112, 10.583 and 10.583
 The square root of 112 is an irrational number that is nonterminating.
 There will be n/2 digits in the square root of an even number with n digits.
 There will be (n+2)/2 digits in the square root of an odd number with n digits.
Challenging Questions
 What is the square root of 112 up to 6 decimal places? (Use long division)
 Find the square root of the following numbers:
 11200
 0.112
Solved Examples

Example 1: Charles wants to calculate the side length of his right triangleshaped garden. The hypotenuse and one side measure 10 and 8 centimeters respectively.
Solution:
Hypotenuse = 10 cm = h
Side 1 = 8 cm = a
Side 2 = b
To find the third side we need to use the formula, h^{2 }= a^{2} + b^{2}
b^{2}^{ }= h^{2}  a^{2 }= 10^{2}  8^{2} = 100  64 = 36
b= √36 = 6Therefore, the side length measures 6 units.

Example 2: What is the radius of a circle having an area of 112π square inches?
Solution:
The area is found using the formula of the area of a circle, which is πr^{2}. By the given information,
πr^{2} = 112π
r^{2} = 112
r = 10.583Therefore, the radius of the circle is ≅ 10.6 inches
FAQs on Square Root of 112
What is the prime factorization of 112?
Prime factorization of 112: 2^{4} × 7
Is 112 a perfect square?
112 is not a perfect square. 112 is a natural number, but since there is no other natural number that can be squared to result in the number 112, it is NOT a perfect square.
What is the simplified form of the square root of 112?
The simplified form of the square root of 112 is 4√7.
What is the decimal value of the square root of 112?
The decimal value of the square root of 112 is 10.583.
Is the square root of 112 a rational number?
No, the square root of 112 is not a rational number since the square root of 112 is nonterminating and cannot be represented in the form of p/q.
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