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Square Root of 299

The square root of 299 is expressed as √299 in the radical form and as (299)^½ or (299)^0.5 in the exponent form. The square root of 299 rounded up to 8 decimal places is 17.29161647. It is the positive solution of the equation x² = 299.

Square Root of 299: 17.291616465790582
Square Root of 299 in exponential form: (299)^½ or (299)^0.5
Square Root of 299 in radical form: √299

Square Root of 299

1.	What is the Square Root of 299?
2.	How to find the Square Root of 299?
3.	Is the Square Root of 299 Irrational?
4.	FAQs

What is the Square Root of 299?

The square root of 299, (or root 299), is the number which when multiplied by itself gives the product as 299. Therefore, the square root of 299 = √299 = 17.291616465790582.

☛ Check: Square Root Calculator

How to Find Square Root of 299?

Square Root of 299 by Long Division Method

Value of √299 by Long Division Method

Explanation:

Forming pairs: 02 and 99
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 99, to the right of the remainder 1. The new dividend is now 199.
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 <= 199. After finding Z, together 2 and Z (7) form a new divisor 27 for the new dividend 199.
Divide 199 by 27 with the quotient as 7, giving the remainder = 199 - 27 × 7 = 199 - 189 = 10.
Now, let's find the decimal places after the quotient 17.
Bring down 00 to the right of this remainder 10. The new dividend is now 1000.
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 <= 1000. Together they form a new divisor (342) for the new dividend (1000).
Divide 1000 by 342 with the quotient as 2, giving the remainder = 1000 - 342 × 2 = 1000 - 684 = 316.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 299.

Therefore, the square root of 299 by long division method is 17.2 approx.

Is Square Root of 299 Irrational?

The actual value of √299 is undetermined. The value of √299 up to 25 decimal places is 17.29161646579058264534481. Hence, the square root of 299 is an irrational number.

☛ Also Check:

Square Root of 23 - √23 = 4.79583
Square Root of 289 - √289 = 17
Square Root of 324 - √324 = 18
Square Root of 8 - √8 = 2.82843
Square Root of 361 - √361 = 19
Square Root of 250 - √250 = 15.81139
Square Root of 63 - √63 = 7.93725

Square Root of 299 Solved Examples

Example 1: Solve the equation x² − 299 = 0

Solution:

x² - 299 = 0 i.e. x² = 299
x = ±√299
Since the value of the square root of 299 is 17.292,
⇒ x = +√299 or -√299 = 17.292 or -17.292.
Example 2: If the area of a square is 299 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 = 299 in²
⇒ a = ±√299 in
Since length can't be negative,
⇒ a = √299 = 17.292 in
Example 3: If the area of a circle is 299π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 299π in²
⇒ r = ±√299 in
Since radius can't be negative,
⇒ r = √299
The square root of 299 is 17.292.
⇒ r = 17.292 in

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FAQs on the Square Root of 299

What is the Value of the Square Root of 299?

The square root of 299 is 17.29161.

Why is the Square Root of 299 an Irrational Number?

Upon prime factorizing 299 i.e. 13¹ × 23¹, 13 is in odd power. Therefore, the square root of 299 is irrational.

Is the number 299 a Perfect Square?

The prime factorization of 299 = 13¹ × 23¹. Here, the prime factor 13 is not in the pair. Therefore, 299 is not a perfect square.

If the Square Root of 299 is 17.292. Find the Value of the Square Root of 2.99.

Let us represent √2.99 in p/q form i.e. √(299/100) = 2.99/10 = 1.729. Hence, the value of √2.99 = 1.729

Evaluate 6 plus 9 square root 299

The given expression is 6 + 9 √299. We know that the square root of 299 is 17.292. Therefore, 6 + 9 √299 = 6 + 9 × 17.292 = 6 + 155.625 = 161.625

What is the Square Root of -299?

The square root of -299 is an imaginary number. It can be written as √-299 = √-1 × √299 = i √299 = 17.291i
where i = √-1 and it is called the imaginary unit.

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