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Square Root of 337

The square root of 337 is expressed as √337 in the radical form and as (337)^½ or (337)^0.5 in the exponent form. The square root of 337 rounded up to 9 decimal places is 18.357559751. It is the positive solution of the equation x² = 337.

Square Root of 337: 18.35755975068582
Square Root of 337 in exponential form: (337)^½ or (337)^0.5
Square Root of 337 in radical form: √337

Square Root of 337

1.	What is the Square Root of 337?
2.	How to find the Square Root of 337?
3.	Is the Square Root of 337 Irrational?
4.	FAQs

What is the Square Root of 337?

The square root of 337, (or root 337), is the number which when multiplied by itself gives the product as 337. Therefore, the square root of 337 = √337 = 18.35755975068582.

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How to Find Square Root of 337?

Square Root of 337 by Long Division Method

Value of √337 by Long Division Method

Explanation:

Forming pairs: 03 and 37
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 37, to the right of the remainder 2. The new dividend is now 237.
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 <= 237. After finding Z, together 2 and Z (8) form a new divisor 28 for the new dividend 237.
Divide 237 by 28 with the quotient as 8, giving the remainder = 237 - 28 × 8 = 237 - 224 = 13.
Now, let's find the decimal places after the quotient 18.
Bring down 00 to the right of this remainder 13. The new dividend is now 1300.
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 <= 1300. Together they form a new divisor (363) for the new dividend (1300).
Divide 1300 by 363 with the quotient as 3, giving the remainder = 1300 - 363 × 3 = 1300 - 1089 = 211.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 337.

Therefore, the square root of 337 by long division method is 18.3 approximately.

Is Square Root of 337 Irrational?

The actual value of √337 is undetermined. The value of √337 up to 25 decimal places is 18.35755975068581929849172. Hence, the square root of 337 is an irrational number.

☛ Also Check:

Square Root of 89 - √89 = 9.43398
Square Root of 19 - √19 = 4.35890
Square Root of 77 - √77 = 8.77496
Square Root of 12 - √12 = 3.46410
Square Root of 61 - √61 = 7.81025
Square Root of 2 - √2 = 1.41421
Square Root of 113 - √113 = 10.63015

Square Root of 337 Solved Examples

Example 1: Solve the equation x² − 337 = 0

Solution:

x² - 337 = 0 i.e. x² = 337
x = ±√337
Since the value of the square root of 337 is 18.358,
⇒ x = +√337 or -√337 = 18.358 or -18.358.
Example 2: If the area of a square is 337 in². Find the length of the side of the square.

Solution:

Let 'a' be the length of the side of the square.
⇒ Area of the square = a² = 337 in²
⇒ a = ±√337 in
Since length can't be negative,
⇒ a = √337 = 18.358 in
Example 3: If the area of an equilateral triangle is 337√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 = 337√3 in²
⇒ a = ±√1348 in
Since length can't be negative,
⇒ a = √1348 = 2 √337
We know that the square root of 337 is 18.358.
⇒ a = 36.715 in

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FAQs on the Square Root of 337

What is the Value of the Square Root of 337?

The square root of 337 is 18.35755.

Why is the Square Root of 337 an Irrational Number?

The number 337 is prime. This implies that the number 337 is pairless and is not in the power of 2. Therefore, the square root of 337 is irrational.

What is the Square Root of -337?

The square root of -337 is an imaginary number. It can be written as √-337 = √-1 × √337 = i √337 = 18.357i
where i = √-1 and it is called the imaginary unit.

What is the Value of 1 square root 337?

The square root of 337 is 18.358. Therefore, 1 √337 = 1 × 18.358 = 18.358.

Evaluate 20 plus 20 square root 337

The given expression is 20 + 20 √337. We know that the square root of 337 is 18.358. Therefore, 20 + 20 √337 = 20 + 20 × 18.358 = 20 + 367.151 = 387.151

What is the Square of the Square Root of 337?

The square of the square root of 337 is the number 337 itself i.e. (√337)² = (337)^2/2 = 337.

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