A day full of math games & activities. Find one near you.

Square Root of 255

The square root of 255 is expressed as √255 in the radical form and as (255)^½ or (255)^0.5 in the exponent form. The square root of 255 rounded up to 7 decimal places is 15.9687194. It is the positive solution of the equation x² = 255.

Square Root of 255: 15.968719422671311
Square Root of 255 in exponential form: (255)^½ or (255)^0.5
Square Root of 255 in radical form: √255

Square Root of 255

1.	What is the Square Root of 255?
2.	How to find the Square Root of 255?
3.	Is the Square Root of 255 Irrational?
4.	FAQs

What is the Square Root of 255?

The square root of 255, (or root 255), is the number which when multiplied by itself gives the product as 255. Therefore, the square root of 255 = √255 = 15.968719422671311.

☛ Check: Square Root Calculator

How to Find Square Root of 255?

Square Root of 255 by Long Division Method

Value of √255 by Long Division Method

Explanation:

Forming pairs: 02 and 55
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 55, to the right of the remainder 1. The new dividend is now 155.
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 <= 155. After finding Z, together 2 and Z (5) form a new divisor 25 for the new dividend 155.
Divide 155 by 25 with the quotient as 5, giving the remainder = 155 - 25 × 5 = 155 - 125 = 30.
Now, let's find the decimal places after the quotient 15.
Bring down 00 to the right of this remainder 30. The new dividend is now 3000.
Add the last digit of quotient to divisor i.e. 5 + 25 = 30. To the right of 30, find a digit Z (which is 9) such that 30Z × Z <= 3000. Together they form a new divisor (309) for the new dividend (3000).
Divide 3000 by 309 with the quotient as 9, giving the remainder = 3000 - 309 × 9 = 3000 - 2781 = 219.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 255.

Therefore, the square root of 255 by long division method is 15.9 approximately.

Is Square Root of 255 Irrational?

The actual value of √255 is undetermined. The value of √255 up to 25 decimal places is 15.96871942267131199907025. Hence, the square root of 255 is an irrational number.

☛ Also Check:

Square Root of 52 - √52 = 7.21110
Square Root of 50 - √50 = 7.07107
Square Root of 23 - √23 = 4.79583
Square Root of 140 - √140 = 11.83216
Square Root of 108 - √108 = 10.39230
Square Root of 99 - √99 = 9.94987
Square Root of 98 - √98 = 9.89949

Square Root of 255 Solved Examples

Example 1: Solve the equation x² − 255 = 0

Solution:

x² - 255 = 0 i.e. x² = 255
x = ±√255
Since the value of the square root of 255 is 15.969,
⇒ x = +√255 or -√255 = 15.969 or -15.969.
Example 2: If the surface area of a sphere is 1020π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 1020π in²
⇒ r = ±√255 in
Since radius can't be negative,
⇒ r = √255
The square root of 255 is 15.969.
⇒ r = 15.969 in
Example 3: If the area of a circle is 255π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 255π in²
⇒ r = ±√255 in
Since radius can't be negative,
⇒ r = √255
The square root of 255 is 15.969.
⇒ r = 15.969 in

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on the Square Root of 255

What is the Value of the Square Root of 255?

The square root of 255 is 15.96871.

Why is the Square Root of 255 an Irrational Number?

Upon prime factorizing 255 i.e. 3¹ × 5¹ × 17¹, 3 is in odd power. Therefore, the square root of 255 is irrational.

Is the number 255 a Perfect Square?

The prime factorization of 255 = 3¹ × 5¹ × 17¹. Here, the prime factor 3 is not in the pair. Therefore, 255 is not a perfect square.

What is the Value of 7 square root 255?

The square root of 255 is 15.969. Therefore, 7 √255 = 7 × 15.969 = 111.781.

Evaluate 3 plus 15 square root 255

The given expression is 3 + 15 √255. We know that the square root of 255 is 15.969. Therefore, 3 + 15 √255 = 3 + 15 × 15.969 = 3 + 239.531 = 242.531

What is the Square Root of -255?

The square root of -255 is an imaginary number. It can be written as √-255 = √-1 × √255 = i √255 = 15.968i
where i = √-1 and it is called the imaginary unit.

Math worksheets and
visual curriculum