Square root of 53

We know that square root of 53 is not a perfect square so, the √53 will be 7.28 approximately. 

We can write the square root of 53 is written as √53 in radical form and (53)^1/2 in exponential form. 
 

To find the √53 there are different methods that are involved they are:

i) Prime factorization method

ii) Long division method

iii) Estimation method

Reducing 53 to its prime factor is not possible through factorization methods, as 53 is already a prime number it cannot be broken down anymore.

Step 1: Find out if 53 is a prime number or not. As 53 is a prime number, it holds no other positive divisors besides 1 and 53.

Step 2: Prime factors of 53 are 53 and 1 thus we cannot find its square root by prime factorization method. 
Prime factorization does not apply to the square root of 53.

The long division method is used to find square roots of non-perfect squares, we can find the √53 by using the following steps:

Step 1: From the right side we will start from the 53 and join it with bar above it. Pair Zero from left to right in decimals and makes a pair.

Step 2: Find a number with values smaller than or equal to 53 that takes the form of a square. 7 x 7 is 49, so here it is 7. When we divide 53 by 7, we have quotient 7 and remainder 4.

Step 3: Put in a pair of 0s beneath and write it straight beneath 400.

Step 4: 2 x 7 = 14, write 14 on its right. Something like 400 visualizing a factor that large than the dividend fits here

Step 5: Now, multiply 142 by 2. 

Step 6: Keep repeating it until the quotient repeats itself after a fixed digit.

So,from the above calculations we have the square root of 53 as 7.280
 

The approximation method follows the finding the square of 53 by a near estimate. Here are the steps to find the square root of 53 by approximation:

Step 1: It will discover two perfect squares, of 53. Using the perfect squares 7² = 49, and 8² = 64.

Step 2: The root of 53 is 7< 8, so above 7 and below 8. 53 is near to the square root of 7. 

Step 3: In order to find the decimal fraction we shall be using the expression.

(Upper perfect square - Given number) / (Given number - Lower perfect square) 

 So, the decimal part equals to 4/15 = 0.2666666667 etc.

The square root of 53 can be approximated to be ±7.28.
 

• Diagonal :A diagonal rules are straight ruling that join two particular corners on the same building. 

• Quotient :The quotient is taken to mean the product resulting from division of one number into another.

• Decimal :It means that decimal is a method of numbering the numbers in which it contains integer and rational part.