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Square Root of 338

The square root of 338 is expressed as √338 in the radical form and as (338)^½ or (338)^0.5 in the exponent form. The square root of 338 rounded up to 5 decimal places is 18.38478. It is the positive solution of the equation x² = 338. We can express the square root of 338 in its lowest radical form as 13 √2.

Square Root of 338: 18.384776310850235
Square Root of 338 in exponential form: (338)^½ or (338)^0.5
Square Root of 338 in radical form: √338 or 13 √2

Square Root of 338

1.	What is the Square Root of 338?
2.	How to find the Square Root of 338?
3.	Is the Square Root of 338 Irrational?
4.	FAQs

What is the Square Root of 338?

The square root of 338, (or root 338), is the number which when multiplied by itself gives the product as 338. Therefore, the square root of 338 = √338 = 13 √2 = 18.384776310850235.

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How to Find Square Root of 338?

Square Root of 338 by Long Division Method

Value of √338 by Long Division Method

Explanation:

Forming pairs: 03 and 38
Find a number Y (1) such that whose square is <= 3. Now divide 03 by 1 with quotient as 1.
Bring down the next pair 38, to the right of the remainder 2. The new dividend is now 238.
Add the last digit of the quotient (1) to the divisor (1) i.e. 1 + 1 = 2. To the right of 2, find a digit Z (which is 8) such that 2Z × Z <= 238. After finding Z, together 2 and Z (8) form a new divisor 28 for the new dividend 238.
Divide 238 by 28 with the quotient as 8, giving the remainder = 238 - 28 × 8 = 238 - 224 = 14.
Now, let's find the decimal places after the quotient 18.
Bring down 00 to the right of this remainder 14. The new dividend is now 1400.
Add the last digit of quotient to divisor i.e. 8 + 28 = 36. To the right of 36, find a digit Z (which is 3) such that 36Z × Z <= 1400. Together they form a new divisor (363) for the new dividend (1400).
Divide 1400 by 363 with the quotient as 3, giving the remainder = 1400 - 363 × 3 = 1400 - 1089 = 311.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 338.

Therefore, the square root of 338 by long division method is 18.3 approximately.

Is Square Root of 338 Irrational?

The actual value of √338 is undetermined. The value of √338 up to 25 decimal places is 18.38477631085023563442195. Hence, the square root of 338 is an irrational number.

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Square Root of 116 - √116 = 10.77033
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Square Root of 676 - √676 = 26
Square Root of 16 - √16 = 4
Square Root of 63 - √63 = 7.93725
Square Root of 17 - √17 = 4.12311

Square Root of 338 Solved Examples

Example 1: Solve the equation x² − 338 = 0

Solution:

x² - 338 = 0 i.e. x² = 338
x = ±√338
Since the value of the square root of 338 is 18.385,
⇒ x = +√338 or -√338 = 18.385 or -18.385.
Example 2: If the area of an equilateral triangle is 338√3 in². Find the length of one of the sides of the triangle.

Solution:

Let 'a' be the length of one of the sides of the equilateral triangle.
⇒ Area of the equilateral triangle = (√3/4)a² = 338√3 in²
⇒ a = ±√1352 in
Since length can't be negative,
⇒ a = √1352 = 2 √338
We know that the square root of 338 is 18.385.
⇒ a = 36.770 in
Example 3: If the surface area of a cube is 2028 in². Find the length of the side of the cube.

Solution:

Let 'a' be the length of the side of the cube.
⇒ Area of the cube = 6a² = 2028 in²
⇒ a = ±√338 in
Since length can't be negative,
⇒ a = √338
We know that the square root of 338 is 18.385.
⇒ a = 18.385 in

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FAQs on the Square Root of 338

What is the Value of the Square Root of 338?

The square root of 338 is 18.38477.

Why is the Square Root of 338 an Irrational Number?

Upon prime factorizing 338 i.e. 2¹ × 13², 2 is in odd power. Therefore, the square root of 338 is irrational.

What is the Square Root of -338?

The square root of -338 is an imaginary number. It can be written as √-338 = √-1 × √338 = i √338 = 18.384i
where i = √-1 and it is called the imaginary unit.

What is the Square of the Square Root of 338?

The square of the square root of 338 is the number 338 itself i.e. (√338)² = (338)^2/2 = 338.

If the Square Root of 338 is 18.385. Find the Value of the Square Root of 3.38.

Let us represent √3.38 in p/q form i.e. √(338/100) = 3.38/10 = 1.838. Hence, the value of √3.38 = 1.838

What is the Square Root of 338 in Simplest Radical Form?

We need to express 338 as the product of its prime factors i.e. 338 = 2 × 13 × 13. Therefore, √338 = √2 × 13 × 13 = 13 √2. Thus, the square root of 338 in the lowest radical form is 13 √2.

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