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Square Root of 341

The square root of 341 is expressed as √341 in the radical form and as (341)^½ or (341)^0.5 in the exponent form. The square root of 341 rounded up to 9 decimal places is 18.466185313. It is the positive solution of the equation x² = 341.

Square Root of 341: 18.466185312619388
Square Root of 341 in exponential form: (341)^½ or (341)^0.5
Square Root of 341 in radical form: √341

Square Root of 341

1.	What is the Square Root of 341?
2.	How to find the Square Root of 341?
3.	Is the Square Root of 341 Irrational?
4.	FAQs

What is the Square Root of 341?

The square root of 341, (or root 341), is the number which when multiplied by itself gives the product as 341. Therefore, the square root of 341 = √341 = 18.466185312619388.

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How to Find Square Root of 341?

Square Root of 341 by Long Division Method

Value of √341 by Long Division Method

Explanation:

Forming pairs: 03 and 41
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 41, to the right of the remainder 2. The new dividend is now 241.
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 <= 241. After finding Z, together 2 and Z (8) form a new divisor 28 for the new dividend 241.
Divide 241 by 28 with the quotient as 8, giving the remainder = 241 - 28 × 8 = 241 - 224 = 17.
Now, let's find the decimal places after the quotient 18.
Bring down 00 to the right of this remainder 17. The new dividend is now 1700.
Add the last digit of quotient to divisor i.e. 8 + 28 = 36. To the right of 36, find a digit Z (which is 4) such that 36Z × Z <= 1700. Together they form a new divisor (364) for the new dividend (1700).
Divide 1700 by 364 with the quotient as 4, giving the remainder = 1700 - 364 × 4 = 1700 - 1456 = 244.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 341.

Therefore, the square root of 341 by long division method is 18.4 approx.

Is Square Root of 341 Irrational?

The actual value of √341 is undetermined. The value of √341 up to 25 decimal places is 18.46618531261938787760218. Hence, the square root of 341 is an irrational number.

☛ Also Check:

Square Root of 19 - √19 = 4.35890
Square Root of 49 - √49 = 7
Square Root of 39 - √39 = 6.24500
Square Root of 22 - √22 = 4.69042
Square Root of 68 - √68 = 8.24621
Square Root of 33 - √33 = 5.74456
Square Root of 841 - √841 = 29

Square Root of 341 Solved Examples

Example 1: Solve the equation x² − 341 = 0

Solution:

x² - 341 = 0 i.e. x² = 341
x = ±√341
Since the value of the square root of 341 is 18.466,
⇒ x = +√341 or -√341 = 18.466 or -18.466.
Example 2: If the surface area of a sphere is 1364π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 1364π in²
⇒ r = ±√341 in
Since radius can't be negative,
⇒ r = √341
The square root of 341 is 18.466.
⇒ r = 18.466 in
Example 3: If the area of an equilateral triangle is 341√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 = 341√3 in²
⇒ a = ±√1364 in
Since length can't be negative,
⇒ a = √1364 = 2 √341
We know that the square root of 341 is 18.466.
⇒ a = 36.932 in

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FAQs on the Square Root of 341

What is the Value of the Square Root of 341?

The square root of 341 is 18.46618.

Why is the Square Root of 341 an Irrational Number?

Upon prime factorizing 341 i.e. 11¹ × 31¹, 11 is in odd power. Therefore, the square root of 341 is irrational.

What is the Square Root of -341?

The square root of -341 is an imaginary number. It can be written as √-341 = √-1 × √341 = i √341 = 18.466i
where i = √-1 and it is called the imaginary unit.

If the Square Root of 341 is 18.466. Find the Value of the Square Root of 3.41.

Let us represent √3.41 in p/q form i.e. √(341/100) = 3.41/10 = 1.847. Hence, the value of √3.41 = 1.847

Evaluate 11 plus 12 square root 341

The given expression is 11 + 12 √341. We know that the square root of 341 is 18.466. Therefore, 11 + 12 √341 = 11 + 12 × 18.466 = 11 + 221.594 = 232.594

What is the Square of the Square Root of 341?

The square of the square root of 341 is the number 341 itself i.e. (√341)² = (341)^2/2 = 341.

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