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Square Root of 329

The square root of 329 is expressed as √329 in the radical form and as (329)^½ or (329)^0.5 in the exponent form. The square root of 329 rounded up to 6 decimal places is 18.138357. It is the positive solution of the equation x² = 329.

Square Root of 329: 18.138357147217054
Square Root of 329 in exponential form: (329)^½ or (329)^0.5
Square Root of 329 in radical form: √329

Square Root of 329

1.	What is the Square Root of 329?
2.	How to find the Square Root of 329?
3.	Is the Square Root of 329 Irrational?
4.	FAQs

What is the Square Root of 329?

The square root of 329, (or root 329), is the number which when multiplied by itself gives the product as 329. Therefore, the square root of 329 = √329 = 18.138357147217054.

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How to Find Square Root of 329?

Square Root of 329 by Long Division Method

Value of √329 by Long Division Method

Explanation:

Forming pairs: 03 and 29
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 29, to the right of the remainder 2. The new dividend is now 229.
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 <= 229. After finding Z, together 2 and Z (8) form a new divisor 28 for the new dividend 229.
Divide 229 by 28 with the quotient as 8, giving the remainder = 229 - 28 × 8 = 229 - 224 = 5.
Now, let's find the decimal places after the quotient 18.
Bring down 00 to the right of this remainder 5. The new dividend is now 500.
Add the last digit of quotient to divisor i.e. 8 + 28 = 36. To the right of 36, find a digit Z (which is 1) such that 36Z × Z <= 500. Together they form a new divisor (361) for the new dividend (500).
Divide 500 by 361 with the quotient as 1, giving the remainder = 500 - 361 × 1 = 500 - 361 = 139.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 329.

Therefore, the square root of 329 by long division method is 18.1 approx.

Is Square Root of 329 Irrational?

The actual value of √329 is undetermined. The value of √329 up to 25 decimal places is 18.13835714721705439823295. Hence, the square root of 329 is an irrational number.

☛ Also Check:

Square Root of 15 - √15 = 3.87298
Square Root of 162 - √162 = 12.72792
Square Root of 196 - √196 = 14
Square Root of 80 - √80 = 8.94427
Square Root of 97 - √97 = 9.84886
Square Root of 75 - √75 = 8.66025
Square Root of 36 - √36 = 6

Square Root of 329 Solved Examples

Example 1: Solve the equation x² − 329 = 0

Solution:

x² - 329 = 0 i.e. x² = 329
x = ±√329
Since the value of the square root of 329 is 18.138,
⇒ x = +√329 or -√329 = 18.138 or -18.138.
Example 2: If the area of an equilateral triangle is 329√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 = 329√3 in²
⇒ a = ±√1316 in
Since length can't be negative,
⇒ a = √1316 = 2 √329
We know that the square root of 329 is 18.138.
⇒ a = 36.277 in
Example 3: If the surface area of a cube is 1974 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 = 1974 in²
⇒ a = ±√329 in
Since length can't be negative,
⇒ a = √329
We know that the square root of 329 is 18.138.
⇒ a = 18.138 in

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FAQs on the Square Root of 329

What is the Value of the Square Root of 329?

The square root of 329 is 18.13835.

Why is the Square Root of 329 an Irrational Number?

Upon prime factorizing 329 i.e. 7¹ × 47¹, 7 is in odd power. Therefore, the square root of 329 is irrational.

What is the Square Root of 329 in Simplest Radical Form?

We need to express 329 as the product of its prime factors i.e. 329 = 7 × 47. Therefore, as visible, the radical form of the square root of 329 cannot be simplified further. Therefore, the simplest radical form of the square root of 329 can be written as √329

If the Square Root of 329 is 18.138. Find the Value of the Square Root of 3.29.

Let us represent √3.29 in p/q form i.e. √(329/100) = 3.29/10 = 1.814. Hence, the value of √3.29 = 1.814

Is the number 329 a Perfect Square?

The prime factorization of 329 = 7¹ × 47¹. Here, the prime factor 7 is not in the pair. Therefore, 329 is not a perfect square.

What is the Square Root of -329?

The square root of -329 is an imaginary number. It can be written as √-329 = √-1 × √329 = i √329 = 18.138i
where i = √-1 and it is called the imaginary unit.

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