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Square Root of 38

The square root of 38 is expressed as √38 in the radical form and as (38)^½ or (38)^0.5 in the exponent form. The square root of 38 rounded up to 5 decimal places is 6.16441. It is the positive solution of the equation x² = 38.

Square Root of 38: 6.164414002968976
Square Root of 38 in exponential form: (38)^½ or (38)^0.5
Square Root of 38 in radical form: √38

1.	What Is the Square Root of 38?
2.	Is Square Root of 38 Rational or Irrational?
3.	How to Find the Square Root of 38?
4.	Important Notes
5.	FAQs on Square Root of 38
6.	Challenging Questions

What Is the Square Root of 38?

The square root of a number n is written as √n. This number when squared or multiplied by itself results in the original number n. The square root of 38 can be written in multiple ways:

Radical form: √38
Decimal form: 6.164
Exponent form: (38)^1/2

Is Square Root of 38 Rational or Irrational?

38 is a number which is not a perfect square, which means it does not have a natural number as its square root.
Also, its square root cannot be expressed as a fraction of the form p/q which tells us that the square root of 38 is an irrational number.

How to Find the Square Root of 38?

There are multiple ways to find the square root of 38:

Long Division Method
Estimation and Approximation

One can find out more about these methods by clicking here.

Long Division Method

The square root of 38 by long division method consists of the following steps:

Step 1: Starting from the right, we will pair up the digits of 38 by putting a bar above them. We also pair the 0s in decimals from left to right.
Step 2: Find a number which, when multiplied to itself, gives a product less than or equal to 38. The number 6 fits here as 6 square gives 36. Dividing 38 by 6 with quotient as 6, we get the remainder as 2.
Step 3: Drag a pair of 0s down and fill it next to 2 to make the dividend 200.
Step 4: Double the divisor 6, and enter 12 below with a blank digit on its right. Guess the largest possible digit (X) to fill in the blank and the quotient for which the product of 12X × X results in a value less than or equal to 200. This will be 1 in this case, so divide 200 with 121 and write the remainder.
Step 5: Repeat this process to get the decimal places you want.

Square root of 38

Therefore, the square root of 38 = 6.164

Estimation and Approximation

The estimation method gives us an approximate answer and is usually not accurate to more than 1 decimal place. However, it is easy to perform as can be seen under.

First, we will find the two consecutive numbers such that 38 lies between their perfect squares.
In this case, the numbers are 6 (36) and 7 (49).
We take the whole number part to be the smaller perfect square, in this case 6.
Now, for the decimal part we will use the below formula:
(Given number - Smaller perfect square) / (Greater perfect square - smaller perfect square)
= (38 - 36)/(49 - 36) = 2/13 = 0.15
Therefore, we can estimate the square root of 38 ≅ 6.15

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Important Notes

The square root of 38 is an irrational number.
The number 38 is not a perfect square.
The square root of -38 is an imaginary number.

Challenging Questions

What is the square root of 38 up to 5 decimal places? (Use long division)
Find the square root of the following numbers:
- 3838
- 0.38

Solved Examples

Example 1: What is the square root of -√38?

Solution:

The square root of negative numbers is represented by imaginary numbers.
So, the square root of -√38 is written as √38 i. Where (i = -√1)
Example 2: Richard wants to buy a new wall painting. In the store, he finds a square painting that has an area of 1444 sq units. How long is each side of the painting?

Solution:

To find the side of the painting, we will have to find the square root of 1444.
The square root is √1444 = 38.
Hence, the side length of the painting is 38 units.
Example: If the surface area of a sphere is 152π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 152π in²
⇒ r = ±√38 in
Since radius can't be negative,
⇒ r = √38
The square root of 38 is 6.164.
⇒ r = 6.164 in

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FAQs on the Square Root of 38

What is the Value of the Square Root of 38?

The square root of 38 is 6.16441.

Why is the Square Root of 38 an Irrational Number?

Upon prime factorizing 38 i.e. 2¹ × 19¹, 2 is in odd power. Therefore, the square root of 38 is irrational.

Evaluate 15 plus 12 square root 38

The given expression is 15 + 12 √38. We know that the square root of 38 is 6.164. Therefore, 15 + 12 √38 = 15 + 12 × 6.164 = 15 + 73.973 = 88.973

What is the Square Root of 38 in Simplest Radical Form?

We need to express 38 as the product of its prime factors i.e. 38 = 2 × 19. Therefore, as visible, the radical form of the square root of 38 cannot be simplified further. Therefore, the simplest radical form of the square root of 38 can be written as √38

What is the Value of 19 square root 38?

The square root of 38 is 6.164. Therefore, 19 √38 = 19 × 6.164 = 117.124.

What is the Square of the Square Root of 38?

The square of the square root of 38 is the number 38 itself i.e. (√38)² = (38)^2/2 = 38.

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