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Square Root of 62
The square root of 62 is a number which when multiplied by itself, results in the number 62. The square root is an important part of mathematics which one will use at some point in their life. Without saying more, let us see how to calculate the value of the square root of 62 and see some problems to help us understand this topic.
Square Root of 62: √62 = 7.87400787...
Square of 62: 62^{2} = 3844
1.  What is the Square Root of 62? 
2.  Is Square Root of 62 Rational or Irrational? 
3.  How to Find the Square Root of 62? 
4.  FAQs on Square Root of 62 
What is the Square Root of 62?
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 62 can be written in multiple ways
 Radical form: √62
 Decimal form: 7.874
 Exponent form: (62)^{1/2}
Is Square Root of 62 Rational or Irrational?
 62 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 confirms to us that the square root of 62 is an irrational number.
How to Find the Square Root of 62?
There are multiple ways to find the square root of 62
 Long Division
 Estimation and Approximation
One can find out more about these methods by clicking here
Long Division Method
The square root of 62 by long division method consists of the following steps:
 Step 1: Starting from the right, we will pair up the digits 62 by putting a bar above them. We also pair the 0s in decimals in pairs of 2 from left to right.
 Step 2: Find a number that, when multiplied to itself, gives a product less than or equal to 62. The number 7 fits here as 7 squared gives 49. Dividing 62 by 7 with quotient of 7, we get the remainder as 13.
 Step 3: Drag a pair of 0’s down and fill it next to the remainder to make the dividend 1300.
 Step 4: Double the divisor 7, and enter 14 below with a blank digit on its right. Guess the largest possible digit(X) to fill in the blank and the quotient for which the product of 14X × X results in a value less than or equal to 1300. This will be 8 in this case, so divide 1400 with 168 and write the remainder.
 Step 5: Repeat this process to get the decimal places you want.
Therefore, the square root of 62 = 7.874
Estimation and Approximation
The estimation method gives us an approximate answer and is usually not accurate to more than 1 decimal place. However, it is easy to perform as can be seen under.
 Step 1: Find a perfect square that is smaller than and bigger than 62. In this case, 7 and 8 will work as their squares are 49 and 64.
 Step 2: Writing in terms of inequality: 7 < √62 < 8 = 49 < 62 < 64
 Step 3: Multiply by 10 and write in terms of square roots: √4900 < √6200 < √6400
 Step 4: Move closer to inequality: √6084 < √6200 < √6241 = 78 < 10√62 < 79 = 7.8 < √62 < 7.9
 Step 5: Taking the average of upper and lower limits we get, (7.8 + 7.9)/2 = 7.85
Therefore, we can estimate the square root of 62 ≅ 7.85
Explore Square roots using illustrations and interactive examples
Important Notes
 There exists a positive and negative root of 62, 7.874 and 7.874.
 The square root of 62 is an irrational number that is nonterminating.
Challenging Questions
 What is the square root of 62 up to 6 decimal places(Use Long Division)?
 Find the square root of the following numbers:
 6262
 0.0062
Solved Examples

Example 1: Jake wants to calculate the side length of his square courtyard in his home. It has an area of 62 square feet.
Solution:
To find the side of the courtyard, we will have to find the square root of 62. The square root is √62 = 7.874.
Hence, the side length of the courtyard is approximately 7.9 feet. 
Example 2: Gary was asked to solve an equation x^{2}  62 = 0. Help him find all values of x
Solution:
x^{2}  62 = 0
x^{2} = 62.
Taking the square root on both sides, we get
x = ±7.874
FAQs on Square Root of 62
What is the prime factorization of 62?
The prime factorization of 62 is 2 × 31.
Is 62 a perfect square root?
62 is not a perfect square. 62 is a natural number, but since there is no other natural number that can be squared to result in the number 62, it is NOT a perfect square.
What is the decimal value of the square root of 62?
The decimal value of the square root of 62 is 7.874.
Is the square root of 62 a rational number?
No, the square root of 62 is not a rational number since the square root of 62 is nonterminating and cannot be represented in the form of p/q.
Can we find the square root of 62 by the repeated subtraction method?
No, we can’t find the square root of 62 by repeated subtraction method as it can be used only for perfect squares. 62 is not a perfect square.
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