211 LearnersLast updated on May 26th, 2025
Square root of 38
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.
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.
Mistake 1
Rounding the numbers too soon
Rounding 6.16441 to 6.0 too early can result in inaccuracies when applying the square root.
Square root of 38 Examples
Problem 1
Simplify 4√38+5√38.Combine the terms and simplify the expression.
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.
Problem 2
If y=√38, find y³+2y²
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.
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.
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.
FAQs on the Square root of 38
1.What is the square of 38?
2.What is the value of √37?
3.Is 70 a perfect square?
4. Is 45 a perfect square?
5. What is √66?
6.How can children in India use numbers in everyday life to understand Square root of 38 ?
7.What are some fun ways kids in India can practice Square root of 38 with numbers?
8.What role do numbers and Square root of 38 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Square root of 38 skills?
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.
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