Square root of 37

The square root is the number that gives the original number when squared. 

√37 = 6.08276253 in exponential form, it is written as √37 =37^1/2.

In this article we will learn more about the square root of 37, how to find it and common mistakes one may make when trying to find the square root. 

To find the square root of a number of students learn many methods. When a number is a perfect square and the process of finding square root is simple. 
 

Breakdown 37 into prime factors, group them and the result is the square root.

Prime factorization of 37; 

37= 37×1

All prime factors cannot be paired and 37 cannot be simplified to a perfect square. Hence, the square root of 37 cannot be expressed in simple radical form.√37 is irrational. 
 

For non-perfect squares, we often use the nearest perfect square value to find the value of a square root. Follow the below steps; 

Step 1: Pair 37 with zeros, as it has no decimals in it.

37.00→ (37)(00) 

Step 2: pick a number whose square is ≤ 37, 6²=36

— 6 is the quotient. 

— Subtract the numbers, 37-36=1. 

— Bring down the numbers next to the remainder.

Step 3: double quotient and use it as the first digit of the new divisor’s

— Double 6

— Now find the digit x in a way that 2x×x ≤ 100

— x is 9, 29×9 = 261.

Step 4: Now find the final quotient 

The result; √37 = 6.0827 
 

In the approximation method, we estimate the square root by considering the closest perfect square to 37. 
Follow the below steps; 

Step 1: Nearest perfect square to 37 → √36=6 and √49 = 7 

Step 2: 37 falls between 36 and 49 therefore the square root falls between 6 and 7

Step 3: We try to test numbers like 6.1,6.08 and further. We find that √37 = 6.0827.

• Prime numbers — Any number that has only two factors, 1 and the number itself, is called a prime number. Prime numbers up to 10 are — 2,3,5,7.

• Integer — A number between zero and infinite, that can be positive or negative, fraction or decimal. 

• Perfect square number — a number whose square root has no decimal places in them. For example, the square root of 37. 

• Non-perfect square numbers — A number whose square has a fraction or decimal in its result. For example, square root of 37.