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Square Root of 528

The square root of 528 is expressed as √528 in the radical form and as (528)^½ or (528)^0.5 in the exponent form. The square root of 528 rounded up to 10 decimal places is 22.9782505862. It is the positive solution of the equation x² = 528. We can express the square root of 528 in its lowest radical form as 4 √33.

Square Root of 528: 22.978250586152114
Square Root of 528 in exponential form: (528)^½ or (528)^0.5
Square Root of 528 in radical form: √528 or 4 √33

Square Root of 528

1.	What is the Square Root of 528?
2.	How to find the Square Root of 528?
3.	Is the Square Root of 528 Irrational?
4.	FAQs

What is the Square Root of 528?

The square root of 528, (or root 528), is the number which when multiplied by itself gives the product as 528. Therefore, the square root of 528 = √528 = 4 √33 = 22.978250586152114.

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How to Find Square Root of 528?

Square Root of 528 by Long Division Method

Value of √528 by Long Division Method

Explanation:

Forming pairs: 05 and 28
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 28, to the right of the remainder 1. The new dividend is now 128.
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 <= 128. After finding Z, together 4 and Z (2) form a new divisor 42 for the new dividend 128.
Divide 128 by 42 with the quotient as 2, giving the remainder = 128 - 42 × 2 = 128 - 84 = 44.
Now, let's find the decimal places after the quotient 22.
Bring down 00 to the right of this remainder 44. The new dividend is now 4400.
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 <= 4400. Together they form a new divisor (449) for the new dividend (4400).
Divide 4400 by 449 with the quotient as 9, giving the remainder = 4400 - 449 × 9 = 4400 - 4041 = 359.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 528.

Therefore, the square root of 528 by long division method is 22.9 approximately.

Is Square Root of 528 Irrational?

The actual value of √528 is undetermined. The value of √528 up to 25 decimal places is 22.97825058615211463940245. Hence, the square root of 528 is an irrational number.

☛ Also Check:

Square Root of 900 - √900 = 30
Square Root of 1681 - √1681 = 41
Square Root of 92 - √92 = 9.59166
Square Root of 29 - √29 = 5.38516
Square Root of 44 - √44 = 6.63325
Square Root of 26 - √26 = 5.09902
Square Root of 96 - √96 = 9.79796

Square Root of 528 Solved Examples

Example 1: Solve the equation x² − 528 = 0

Solution:

x² - 528 = 0 i.e. x² = 528
x = ±√528
Since the value of the square root of 528 is 22.978,
⇒ x = +√528 or -√528 = 22.978 or -22.978.
Example 2: If the surface area of a sphere is 2112π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 2112π in²
⇒ r = ±√528 in
Since radius can't be negative,
⇒ r = √528
The square root of 528 is 22.978.
⇒ r = 22.978 in
Example 3: If the surface area of a cube is 3168 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 = 3168 in²
⇒ a = ±√528 in
Since length can't be negative,
⇒ a = √528
We know that the square root of 528 is 22.978.
⇒ a = 22.978 in

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FAQs on the Square Root of 528

What is the Value of the Square Root of 528?

The square root of 528 is 22.97825.

Why is the Square Root of 528 an Irrational Number?

Upon prime factorizing 528 i.e. 2⁴ × 3¹ × 11¹, 3 is in odd power. Therefore, the square root of 528 is irrational.

Evaluate 6 plus 11 square root 528

The given expression is 6 + 11 √528. We know that the square root of 528 is 22.978. Therefore, 6 + 11 √528 = 6 + 11 × 22.978 = 6 + 252.761 = 258.761

What is the Square Root of 528 in Simplest Radical Form?

We need to express 528 as the product of its prime factors i.e. 528 = 2 × 2 × 2 × 2 × 3 × 11. Therefore, √528 = √2 × 2 × 2 × 2 × 3 × 11 = 4 √33. Thus, the square root of 528 in the lowest radical form is 4 √33.

What is the Square of the Square Root of 528?

The square of the square root of 528 is the number 528 itself i.e. (√528)² = (528)^2/2 = 528.

If the Square Root of 528 is 22.978. Find the Value of the Square Root of 5.28.

Let us represent √5.28 in p/q form i.e. √(528/100) = 5.28/10 = 2.298. Hence, the value of √5.28 = 2.298

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