Last updated on May 26th, 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.
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.
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.
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.
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
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.
Students make errors when learning to find the square root of a number. Here are errors and tips to avoid them.
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
The terms are combined by factoring out the common √38, simplifying to 9√38.
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
By approximating y, we calculate y3+2y2 step by step to get an approximate result.
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.
By taking the square root of the area, we find the side length. Applying the perimeter formula, we get the solution.