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Square Root of 349

The square root of 349 is expressed as √349 in the radical form and as (349)^½ or (349)^0.5 in the exponent form. The square root of 349 rounded up to 9 decimal places is 18.681541692. It is the positive solution of the equation x² = 349.

Square Root of 349: 18.681541692269406
Square Root of 349 in exponential form: (349)^½ or (349)^0.5
Square Root of 349 in radical form: √349

Square Root of 349

1.	What is the Square Root of 349?
2.	How to find the Square Root of 349?
3.	Is the Square Root of 349 Irrational?
4.	FAQs

What is the Square Root of 349?

The square root of 349, (or root 349), is the number which when multiplied by itself gives the product as 349. Therefore, the square root of 349 = √349 = 18.681541692269406.

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How to Find Square Root of 349?

Square Root of 349 by Long Division Method

Value of √349 by Long Division Method

Explanation:

Forming pairs: 03 and 49
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 49, to the right of the remainder 2. The new dividend is now 249.
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 <= 249. After finding Z, together 2 and Z (8) form a new divisor 28 for the new dividend 249.
Divide 249 by 28 with the quotient as 8, giving the remainder = 249 - 28 × 8 = 249 - 224 = 25.
Now, let's find the decimal places after the quotient 18.
Bring down 00 to the right of this remainder 25. The new dividend is now 2500.
Add the last digit of quotient to divisor i.e. 8 + 28 = 36. To the right of 36, find a digit Z (which is 6) such that 36Z × Z <= 2500. Together they form a new divisor (366) for the new dividend (2500).
Divide 2500 by 366 with the quotient as 6, giving the remainder = 2500 - 366 × 6 = 2500 - 2196 = 304.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 349.

Therefore, the square root of 349 by long division method is 18.6 approximately.

Is Square Root of 349 Irrational?

The actual value of √349 is undetermined. The value of √349 up to 25 decimal places is 18.68154169226940434847082. Hence, the square root of 349 is an irrational number.

☛ Also Check:

Square Root of 22 - √22 = 4.69042
Square Root of 97 - √97 = 9.84886
Square Root of 900 - √900 = 30
Square Root of 625 - √625 = 25
Square Root of 320 - √320 = 17.88854
Square Root of 12 - √12 = 3.46410
Square Root of 28 - √28 = 5.29150

Square Root of 349 Solved Examples

Example 1: Solve the equation x² − 349 = 0

Solution:

x² - 349 = 0 i.e. x² = 349
x = ±√349
Since the value of the square root of 349 is 18.682,
⇒ x = +√349 or -√349 = 18.682 or -18.682.
Example 2: If the surface area of a sphere is 1396π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 1396π in²
⇒ r = ±√349 in
Since radius can't be negative,
⇒ r = √349
The square root of 349 is 18.682.
⇒ r = 18.682 in
Example 3: If the surface area of a cube is 2094 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 = 2094 in²
⇒ a = ±√349 in
Since length can't be negative,
⇒ a = √349
We know that the square root of 349 is 18.682.
⇒ a = 18.682 in

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FAQs on the Square Root of 349

What is the Value of the Square Root of 349?

The square root of 349 is 18.68154.

Why is the Square Root of 349 an Irrational Number?

The number 349 is prime. This implies that the number 349 is pairless and is not in the power of 2. Therefore, the square root of 349 is irrational.

If the Square Root of 349 is 18.682. Find the Value of the Square Root of 3.49.

Let us represent √3.49 in p/q form i.e. √(349/100) = 3.49/10 = 1.868. Hence, the value of √3.49 = 1.868

Evaluate 13 plus 16 square root 349

The given expression is 13 + 16 √349. We know that the square root of 349 is 18.682. Therefore, 13 + 16 √349 = 13 + 16 × 18.682 = 13 + 298.905 = 311.905

Is the number 349 a Perfect Square?

The number 349 is prime. This implies that the square root of 349 cannot be expressed as a product of two equal integers. Therefore, the number 349 is not a perfect square.

What is the Square of the Square Root of 349?

The square of the square root of 349 is the number 349 itself i.e. (√349)² = (349)^2/2 = 349.

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