Square root of 38
2026-02-28 06:04 Diff
https://brightchamps.com/en-us/math/numbers/square-root-of-38

565 Learners

Last updated on August 5, 2025

Square root is simply a number value that when multiplied with itself gives the original number. We apply square roots when we make financial estimations and solve practical problems in geometry.

What is the square root of 38?

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


√38 = 6.16441400297 in exponential form it is written as√38 =381/2.


In this article we will learn more about the square root of 38, how to find it and common mistakes one may make when trying to find the square root. 

Finding the square root of 38

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

Square root of 38 using the prime factorization method

Breakdown 38 into prime factors, group them and the result is the square root. 


Prime factorization of 38; 


38= 2×19


All prime factors cannot form pairs. We cannot simplify this further. Hence, the square root of 38 cannot be expressed in simple radical form.√38 is irrational. 
 

Explore Our Programs

Square root of 38 using the division method

Pair the digits, begin with the largest square and continue the subtraction and division till we find the result which is the square root of the number. 


Step 1: Pair 38 with zeros as it has no decimals in it.


38.00→ (38)(00) 


Step 2: pick a number whose square is ≤ 38, 62=36


— 6 is the quotient. 


— Subtract the numbers, 38-36=2. 


— 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 ≤ 200


— x is 1, 121×1 = 121.


Step 4: Now find the final quotient 


The result; √38 =  6.16441

Square root of 38 using the approximation method

In the approximation method, we estimate the square root by considering the closest perfect square to 38. 


Follow the below steps; 


Step 1: Nearest perfect square to 38 → √36=6 and √49 = 7 


Step 2: 38 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 √38 =  6.16441.
 

Common Mistakes and How to Avoid Them in the Square Root of 38

Students make errors when learning to find the square root of a number. Here are errors and tips to avoid them. 
 

Download Worksheets

Problem 1

Simplify 4√38+5√38.Combine the terms and simplify the expression.

Okay, lets begin

Both terms have √38​ as a common factor, so factor it out: 


4√38+5√38=√38(4+5)=9√38
 

Explanation

The terms are combined by factoring out the common √38, simplifying to 9√38.
 

Well explained 👍

Problem 2

If y=√38​, find y³+2y²

Okay, lets begin

Approximate y≈6.16, then compute each term: 


y2≈(6.16)2=38, y3≈(6.16)3=234.8


Now compute y3+2y2: 


y3+2y2≈234.85+2(38)2=234.85+76=310.85
 

Explanation

By approximating y, we calculate y3+2y2 step by step to get an approximate result.
 

Well explained 👍

Problem 3

You are tasked with designing a square garden whose area is 38 m². You want to place a fence around the garden and need to calculate the perimeter of the garden. However, you can only use approximate methods for non-perfect square roots.

Okay, lets begin

1. Finding the square root of 38


— The two closest perfect squares to 38 are 36 (√36 = 6) and 49 (√49 = 7).


— Using approximation methods like trial and error, we estimate:


√38≈6.16


(Exact calculation yields √38 ≈ 6.164).


2. Calculating the perimeter of a square is given by:


P=4×side length


Substituting the approximate side length of the garden:


P≈4×6.16=24.64 

Answer: The perimeter of the garden is approximately 24.64 meters.
 

Explanation

By taking the square root of the area, we find the side length. Applying the perimeter formula, we get the solution.
 

Well explained 👍

FAQs on the Square root of 38

1.What is the square of 38?

—Multiplying 38 with 38 is how we find the square of a number, 1444 is the square of 38. 
 

2.What is the value of √37?

— When we simplify for √37, break the number down to factors that include a perfect square. 
By approximation, we get 6.0827.
 

3.Is 70 a perfect square?

—70 is not a perfect square. Perfect square is a number that we get after squaring an integer. 
 

4. Is 45 a perfect square?

— 45 is not a perfect square. Perfect square is a number that we get after squaring an integer. 
 

5. What is √66?

—When we simplify for √66, break the number down to factors that include a perfect square. 
By approximating, we get 8.124.
 

Important glossaries for the square root of 38

  • Prime numbers —  a number whose factors are itself and 1 
  • Integer — A number between zero and infinite, that can be in any form; positive or negative, whole or decimal
  • Perfect square number — any number with non decimals in its square root 
  • Non-perfect square numbers — A number whose square is represented as a  fraction or decimal in its result. 
     

What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math

▶