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

Square Root of 265

The square root of 265 is expressed as √265 in the radical form and as (265)^½ or (265)^0.5 in the exponent form. The square root of 265 rounded up to 5 decimal places is 16.27882. It is the positive solution of the equation x² = 265.

Square Root of 265: 16.278820596099706
Square Root of 265 in exponential form: (265)^½ or (265)^0.5
Square Root of 265 in radical form: √265

Square Root of 265

1.	What is the Square Root of 265?
2.	How to find the Square Root of 265?
3.	Is the Square Root of 265 Irrational?
4.	FAQs

What is the Square Root of 265?

The square root of 265, (or root 265), is the number which when multiplied by itself gives the product as 265. Therefore, the square root of 265 = √265 = 16.278820596099706.

☛ Check: Square Root Calculator

How to Find Square Root of 265?

Square Root of 265 by Long Division Method

Value of √265 by Long Division Method

Explanation:

Forming pairs: 02 and 65
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 65, to the right of the remainder 1. The new dividend is now 165.
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 6) such that 2Z × Z <= 165. After finding Z, together 2 and Z (6) form a new divisor 26 for the new dividend 165.
Divide 165 by 26 with the quotient as 6, giving the remainder = 165 - 26 × 6 = 165 - 156 = 9.
Now, let's find the decimal places after the quotient 16.
Bring down 00 to the right of this remainder 9. The new dividend is now 900.
Add the last digit of quotient to divisor i.e. 6 + 26 = 32. To the right of 32, find a digit Z (which is 2) such that 32Z × Z <= 900. Together they form a new divisor (322) for the new dividend (900).
Divide 900 by 322 with the quotient as 2, giving the remainder = 900 - 322 × 2 = 900 - 644 = 256.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 265.

Therefore, the square root of 265 by long division method is 16.2 approximately.

Is Square Root of 265 Irrational?

The actual value of √265 is undetermined. The value of √265 up to 25 decimal places is 16.27882059609970638735302. Hence, the square root of 265 is an irrational number.

☛ Also Check:

Square Root of 42 - √42 = 6.48074
Square Root of 68 - √68 = 8.24621
Square Root of 8 - √8 = 2.82843
Square Root of 120 - √120 = 10.95445
Square Root of 11 - √11 = 3.31662
Square Root of 841 - √841 = 29
Square Root of 108 - √108 = 10.39230

Square Root of 265 Solved Examples

Example 1: Solve the equation x² − 265 = 0

Solution:

x² - 265 = 0 i.e. x² = 265
x = ±√265
Since the value of the square root of 265 is 16.279,
⇒ x = +√265 or -√265 = 16.279 or -16.279.
Example 2: If the area of a circle is 265π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 265π in²
⇒ r = ±√265 in
Since radius can't be negative,
⇒ r = √265
The square root of 265 is 16.279.
⇒ r = 16.279 in
Example 3: If the surface area of a cube is 1590 in². Find the length of the side of the cube.

Solution:

Let 'a' be the length of the side of the cube.
⇒ Area of the cube = 6a² = 1590 in²
⇒ a = ±√265 in
Since length can't be negative,
⇒ a = √265
We know that the square root of 265 is 16.279.
⇒ a = 16.279 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 265

What is the Value of the Square Root of 265?

The square root of 265 is 16.27882.

Why is the Square Root of 265 an Irrational Number?

Upon prime factorizing 265 i.e. 5¹ × 53¹, 5 is in odd power. Therefore, the square root of 265 is irrational.

Evaluate 18 plus 11 square root 265

The given expression is 18 + 11 √265. We know that the square root of 265 is 16.279. Therefore, 18 + 11 √265 = 18 + 11 × 16.279 = 18 + 179.067 = 197.067

What is the Square of the Square Root of 265?

The square of the square root of 265 is the number 265 itself i.e. (√265)² = (265)^2/2 = 265.

If the Square Root of 265 is 16.279. Find the Value of the Square Root of 2.65.

Let us represent √2.65 in p/q form i.e. √(265/100) = 2.65/10 = 1.628. Hence, the value of √2.65 = 1.628

Is the number 265 a Perfect Square?

The prime factorization of 265 = 5¹ × 53¹. Here, the prime factor 5 is not in the pair. Therefore, 265 is not a perfect square.

Math worksheets and
visual curriculum