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Square Root of 297

The square root of 297 is expressed as √297 in the radical form and as (297)^½ or (297)^0.5 in the exponent form. The square root of 297 rounded up to 9 decimal places is 17.233687940. It is the positive solution of the equation x² = 297. We can express the square root of 297 in its lowest radical form as 3 √33.

Square Root of 297: 17.233687939614086
Square Root of 297 in exponential form: (297)^½ or (297)^0.5
Square Root of 297 in radical form: √297 or 3 √33

Square Root of 297

1.	What is the Square Root of 297?
2.	How to find the Square Root of 297?
3.	Is the Square Root of 297 Irrational?
4.	FAQs

What is the Square Root of 297?

The square root of 297, (or root 297), is the number which when multiplied by itself gives the product as 297. Therefore, the square root of 297 = √297 = 3 √33 = 17.233687939614086.

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How to Find Square Root of 297?

Square Root of 297 by Long Division Method

Value of √297 by Long Division Method

Explanation:

Forming pairs: 02 and 97
Find a number Y (1) such that whose square is <= 2. Now divide 02 by 1 with quotient as 1.
Bring down the next pair 97, to the right of the remainder 1. The new dividend is now 197.
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 7) such that 2Z × Z <= 197. After finding Z, together 2 and Z (7) form a new divisor 27 for the new dividend 197.
Divide 197 by 27 with the quotient as 7, giving the remainder = 197 - 27 × 7 = 197 - 189 = 8.
Now, let's find the decimal places after the quotient 17.
Bring down 00 to the right of this remainder 8. The new dividend is now 800.
Add the last digit of quotient to divisor i.e. 7 + 27 = 34. To the right of 34, find a digit Z (which is 2) such that 34Z × Z <= 800. Together they form a new divisor (342) for the new dividend (800).
Divide 800 by 342 with the quotient as 2, giving the remainder = 800 - 342 × 2 = 800 - 684 = 116.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 297.

Therefore, the square root of 297 by long division method is 17.2 approximately.

Is Square Root of 297 Irrational?

The actual value of √297 is undetermined. The value of √297 up to 25 decimal places is 17.23368793961408597955183. Hence, the square root of 297 is an irrational number.

☛ Also Check:

Square Root of 36 - √36 = 6
Square Root of 162 - √162 = 12.72792
Square Root of 250 - √250 = 15.81139
Square Root of 400 - √400 = 20
Square Root of 51 - √51 = 7.14143
Square Root of 100 - √100 = 10
Square Root of 85 - √85 = 9.21954

Square Root of 297 Solved Examples

Example 1: Solve the equation x² − 297 = 0

Solution:

x² - 297 = 0 i.e. x² = 297
x = ±√297
Since the value of the square root of 297 is 17.234,
⇒ x = +√297 or -√297 = 17.234 or -17.234.
Example 2: If the area of a square is 297 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 = 297 in²
⇒ a = ±√297 in
Since length can't be negative,
⇒ a = √297 = 17.234 in
Example 3: If the area of a circle is 297π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 297π in²
⇒ r = ±√297 in
Since radius can't be negative,
⇒ r = √297
The square root of 297 is 17.234.
⇒ r = 17.234 in

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FAQs on the Square Root of 297

What is the Value of the Square Root of 297?

The square root of 297 is 17.23368.

Why is the Square Root of 297 an Irrational Number?

Upon prime factorizing 297 i.e. 3³ × 11¹, 3 is in odd power. Therefore, the square root of 297 is irrational.

What is the Value of 20 square root 297?

The square root of 297 is 17.234. Therefore, 20 √297 = 20 × 17.234 = 344.674.

Evaluate 16 plus 19 square root 297

The given expression is 16 + 19 √297. We know that the square root of 297 is 17.234. Therefore, 16 + 19 √297 = 16 + 19 × 17.234 = 16 + 327.440 = 343.440

What is the Square Root of 297 in Simplest Radical Form?

We need to express 297 as the product of its prime factors i.e. 297 = 3 × 3 × 3 × 11. Therefore, √297 = √3 × 3 × 3 × 11 = 3 √33. Thus, the square root of 297 in the lowest radical form is 3 √33.

Is the number 297 a Perfect Square?

The prime factorization of 297 = 3³ × 11¹. Here, the prime factor 3 is not in the pair. Therefore, 297 is not a perfect square.

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