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Square Root of 249

The square root of 249 is expressed as √249 in the radical form and as (249)^½ or (249)^0.5 in the exponent form. The square root of 249 rounded up to 9 decimal places is 15.779733838. It is the positive solution of the equation x² = 249.

Square Root of 249: 15.7797338380595
Square Root of 249 in exponential form: (249)^½ or (249)^0.5
Square Root of 249 in radical form: √249

Square Root of 249

1.	What is the Square Root of 249?
2.	How to find the Square Root of 249?
3.	Is the Square Root of 249 Irrational?
4.	FAQs

What is the Square Root of 249?

The square root of 249, (or root 249), is the number which when multiplied by itself gives the product as 249. Therefore, the square root of 249 = √249 = 15.7797338380595.

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How to Find Square Root of 249?

Square Root of 249 by Long Division Method

Value of √249 by Long Division Method

Explanation:

Forming pairs: 02 and 49
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 49, to the right of the remainder 1. The new dividend is now 149.
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 5) such that 2Z × Z <= 149. After finding Z, together 2 and Z (5) form a new divisor 25 for the new dividend 149.
Divide 149 by 25 with the quotient as 5, giving the remainder = 149 - 25 × 5 = 149 - 125 = 24.
Now, let's find the decimal places after the quotient 15.
Bring down 00 to the right of this remainder 24. The new dividend is now 2400.
Add the last digit of quotient to divisor i.e. 5 + 25 = 30. To the right of 30, find a digit Z (which is 7) such that 30Z × Z <= 2400. Together they form a new divisor (307) for the new dividend (2400).
Divide 2400 by 307 with the quotient as 7, giving the remainder = 2400 - 307 × 7 = 2400 - 2149 = 251.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 249.

Therefore, the square root of 249 by long division method is 15.7 approximately.

Is Square Root of 249 Irrational?

The actual value of √249 is undetermined. The value of √249 up to 25 decimal places is 15.77973383805950004528829. Hence, the square root of 249 is an irrational number.

☛ Also Check:

Square Root of 125 - √125 = 11.18034
Square Root of 34 - √34 = 5.83095
Square Root of 74 - √74 = 8.60233
Square Root of 17 - √17 = 4.12311
Square Root of 512 - √512 = 22.62742
Square Root of 325 - √325 = 18.02776
Square Root of 625 - √625 = 25

Square Root of 249 Solved Examples

Example 1: Solve the equation x² − 249 = 0

Solution:

x² - 249 = 0 i.e. x² = 249
x = ±√249
Since the value of the square root of 249 is 15.780,
⇒ x = +√249 or -√249 = 15.780 or -15.780.
Example 2: If the surface area of a sphere is 996π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 996π in²
⇒ r = ±√249 in
Since radius can't be negative,
⇒ r = √249
The square root of 249 is 15.780.
⇒ r = 15.780 in
Example 3: If the area of a square is 249 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 = 249 in²
⇒ a = ±√249 in
Since length can't be negative,
⇒ a = √249 = 15.780 in

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FAQs on the Square Root of 249

What is the Value of the Square Root of 249?

The square root of 249 is 15.77973.

Why is the Square Root of 249 an Irrational Number?

Upon prime factorizing 249 i.e. 3¹ × 83¹, 3 is in odd power. Therefore, the square root of 249 is irrational.

If the Square Root of 249 is 15.780. Find the Value of the Square Root of 2.49.

Let us represent √2.49 in p/q form i.e. √(249/100) = 2.49/10 = 1.578. Hence, the value of √2.49 = 1.578

What is the Value of 2 square root 249?

The square root of 249 is 15.780. Therefore, 2 √249 = 2 × 15.780 = 31.559.

What is the Square of the Square Root of 249?

The square of the square root of 249 is the number 249 itself i.e. (√249)² = (249)^2/2 = 249.

What is the Square Root of -249?

The square root of -249 is an imaginary number. It can be written as √-249 = √-1 × √249 = i √249 = 15.779i
where i = √-1 and it is called the imaginary unit.

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