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

Square Root of 527

The square root of 527 is expressed as √527 in the radical form and as (527)^½ or (527)^0.5 in the exponent form. The square root of 527 rounded up to 6 decimal places is 22.956481. It is the positive solution of the equation x² = 527.

Square Root of 527: 22.956480566497994
Square Root of 527 in exponential form: (527)^½ or (527)^0.5
Square Root of 527 in radical form: √527

Square Root of 527

1.	What is the Square Root of 527?
2.	How to find the Square Root of 527?
3.	Is the Square Root of 527 Irrational?
4.	FAQs

What is the Square Root of 527?

The square root of 527, (or root 527), is the number which when multiplied by itself gives the product as 527. Therefore, the square root of 527 = √527 = 22.956480566497994.

☛ Check: Square Root Calculator

How to Find Square Root of 527?

Square Root of 527 by Long Division Method

Value of √527 by Long Division Method

Explanation:

Forming pairs: 05 and 27
Find a number Y (2) such that whose square is <= 5. Now divide 05 by 2 with quotient as 2.
Bring down the next pair 27, to the right of the remainder 1. The new dividend is now 127.
Add the last digit of the quotient (2) to the divisor (2) i.e. 2 + 2 = 4. To the right of 4, find a digit Z (which is 2) such that 4Z × Z <= 127. After finding Z, together 4 and Z (2) form a new divisor 42 for the new dividend 127.
Divide 127 by 42 with the quotient as 2, giving the remainder = 127 - 42 × 2 = 127 - 84 = 43.
Now, let's find the decimal places after the quotient 22.
Bring down 00 to the right of this remainder 43. The new dividend is now 4300.
Add the last digit of quotient to divisor i.e. 2 + 42 = 44. To the right of 44, find a digit Z (which is 9) such that 44Z × Z <= 4300. Together they form a new divisor (449) for the new dividend (4300).
Divide 4300 by 449 with the quotient as 9, giving the remainder = 4300 - 449 × 9 = 4300 - 4041 = 259.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 527.

Therefore, the square root of 527 by long division method is 22.9 approx.

Is Square Root of 527 Irrational?

The actual value of √527 is undetermined. The value of √527 up to 25 decimal places is 22.95648056649799270358575. Hence, the square root of 527 is an irrational number.

☛ Also Check:

Square Root of 10 - √10 = 3.16228
Square Root of 512 - √512 = 22.62742
Square Root of 85 - √85 = 9.21954
Square Root of 68 - √68 = 8.24621
Square Root of 26 - √26 = 5.09902
Square Root of 250 - √250 = 15.81139
Square Root of 136 - √136 = 11.66190

Square Root of 527 Solved Examples

Example 1: Solve the equation x² − 527 = 0

Solution:

x² - 527 = 0 i.e. x² = 527
x = ±√527
Since the value of the square root of 527 is 22.956,
⇒ x = +√527 or -√527 = 22.956 or -22.956.
Example 2: If the area of a square is 527 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 = 527 in²
⇒ a = ±√527 in
Since length can't be negative,
⇒ a = √527 = 22.956 in
Example 3: If the surface area of a sphere is 2108π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 2108π in²
⇒ r = ±√527 in
Since radius can't be negative,
⇒ r = √527
The square root of 527 is 22.956.
⇒ r = 22.956 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 527

What is the Value of the Square Root of 527?

The square root of 527 is 22.95648.

Why is the Square Root of 527 an Irrational Number?

Upon prime factorizing 527 i.e. 17¹ × 31¹, 17 is in odd power. Therefore, the square root of 527 is irrational.

Is the number 527 a Perfect Square?

The prime factorization of 527 = 17¹ × 31¹. Here, the prime factor 17 is not in the pair. Therefore, 527 is not a perfect square.

What is the Square Root of 527 in Simplest Radical Form?

We need to express 527 as the product of its prime factors i.e. 527 = 17 × 31. Therefore, as visible, the radical form of the square root of 527 cannot be simplified further. Therefore, the simplest radical form of the square root of 527 can be written as √527

If the Square Root of 527 is 22.956. Find the Value of the Square Root of 5.27.

Let us represent √5.27 in p/q form i.e. √(527/100) = 5.27/10 = 2.296. Hence, the value of √5.27 = 2.296

What is the Value of 2 square root 527?

The square root of 527 is 22.956. Therefore, 2 √527 = 2 × 22.956 = 45.913.

Math worksheets and
visual curriculum