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Square Root of 526

The square root of 526 is expressed as √526 in the radical form and as (526)^½ or (526)^0.5 in the exponent form. The square root of 526 rounded up to 8 decimal places is 22.93468988. It is the positive solution of the equation x² = 526.

Square Root of 526: 22.93468988235943
Square Root of 526 in exponential form: (526)^½ or (526)^0.5
Square Root of 526 in radical form: √526

Square Root of 526

1.	What is the Square Root of 526?
2.	How to find the Square Root of 526?
3.	Is the Square Root of 526 Irrational?
4.	FAQs

What is the Square Root of 526?

The square root of 526, (or root 526), is the number which when multiplied by itself gives the product as 526. Therefore, the square root of 526 = √526 = 22.93468988235943.

☛ Check: Square Root Calculator

How to Find Square Root of 526?

Square Root of 526 by Long Division Method

Value of √526 by Long Division Method

Explanation:

Forming pairs: 05 and 26
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 26, to the right of the remainder 1. The new dividend is now 126.
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 <= 126. After finding Z, together 4 and Z (2) form a new divisor 42 for the new dividend 126.
Divide 126 by 42 with the quotient as 2, giving the remainder = 126 - 42 × 2 = 126 - 84 = 42.
Now, let's find the decimal places after the quotient 22.
Bring down 00 to the right of this remainder 42. The new dividend is now 4200.
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 <= 4200. Together they form a new divisor (449) for the new dividend (4200).
Divide 4200 by 449 with the quotient as 9, giving the remainder = 4200 - 449 × 9 = 4200 - 4041 = 159.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 526.

Therefore, the square root of 526 by long division method is 22.9 approx.

Is Square Root of 526 Irrational?

The actual value of √526 is undetermined. The value of √526 up to 25 decimal places is 22.93468988235942988897378. Hence, the square root of 526 is an irrational number.

☛ Also Check:

Square Root of 68 - √68 = 8.24621
Square Root of 28 - √28 = 5.29150
Square Root of 140 - √140 = 11.83216
Square Root of 50 - √50 = 7.07107
Square Root of 200 - √200 = 14.14214
Square Root of 225 - √225 = 15
Square Root of 49 - √49 = 7

Square Root of 526 Solved Examples

Example 1: Solve the equation x² − 526 = 0

Solution:

x² - 526 = 0 i.e. x² = 526
x = ±√526
Since the value of the square root of 526 is 22.935,
⇒ x = +√526 or -√526 = 22.935 or -22.935.
Example 2: If the surface area of a sphere is 2104π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 2104π in²
⇒ r = ±√526 in
Since radius can't be negative,
⇒ r = √526
The square root of 526 is 22.935.
⇒ r = 22.935 in
Example 3: If the surface area of a cube is 3156 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 = 3156 in²
⇒ a = ±√526 in
Since length can't be negative,
⇒ a = √526
We know that the square root of 526 is 22.935.
⇒ a = 22.935 in

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FAQs on the Square Root of 526

What is the Value of the Square Root of 526?

The square root of 526 is 22.93468.

Why is the Square Root of 526 an Irrational Number?

Upon prime factorizing 526 i.e. 2¹ × 263¹, 2 is in odd power. Therefore, the square root of 526 is irrational.

Is the number 526 a Perfect Square?

The prime factorization of 526 = 2¹ × 263¹. Here, the prime factor 2 is not in the pair. Therefore, 526 is not a perfect square.

Evaluate 5 plus 20 square root 526

The given expression is 5 + 20 √526. We know that the square root of 526 is 22.935. Therefore, 5 + 20 √526 = 5 + 20 × 22.935 = 5 + 458.694 = 463.694

If the Square Root of 526 is 22.935. Find the Value of the Square Root of 5.26.

Let us represent √5.26 in p/q form i.e. √(526/100) = 5.26/10 = 2.293. Hence, the value of √5.26 = 2.293

What is the Square of the Square Root of 526?

The square of the square root of 526 is the number 526 itself i.e. (√526)² = (526)^2/2 = 526.

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