Square Root of 525

The square root of 525 is expressed as √525 in the radical form and as (525)^½ or (525)^0.5 in the exponent form. The square root of 525 rounded up to 10 decimal places is 22.9128784748. It is the positive solution of the equation x² = 525. We can express the square root of 525 in its lowest radical form as 5 √21.

Square Root of 525: 22.9128784747792
Square Root of 525 in exponential form: (525)^½ or (525)^0.5
Square Root of 525 in radical form: √525 or 5 √21

Square Root of 525

1.	What is the Square Root of 525?
2.	How to find the Square Root of 525?
3.	Is the Square Root of 525 Irrational?
4.	FAQs

What is the Square Root of 525?

The square root of 525, (or root 525), is the number which when multiplied by itself gives the product as 525. Therefore, the square root of 525 = √525 = 5 √21 = 22.9128784747792.

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How to Find Square Root of 525?

Square Root of 525 by Long Division Method

Value of √525 by Long Division Method

Explanation:

Forming pairs: 05 and 25
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 25, to the right of the remainder 1. The new dividend is now 125.
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 <= 125. After finding Z, together 4 and Z (2) form a new divisor 42 for the new dividend 125.
Divide 125 by 42 with the quotient as 2, giving the remainder = 125 - 42 × 2 = 125 - 84 = 41.
Now, let's find the decimal places after the quotient 22.
Bring down 00 to the right of this remainder 41. The new dividend is now 4100.
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 <= 4100. Together they form a new divisor (449) for the new dividend (4100).
Divide 4100 by 449 with the quotient as 9, giving the remainder = 4100 - 449 × 9 = 4100 - 4041 = 59.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 525.

Therefore, the square root of 525 by long division method is 22.9 approx.

Is Square Root of 525 Irrational?

The actual value of √525 is undetermined. The value of √525 up to 25 decimal places is 22.91287847477920003294024. Hence, the square root of 525 is an irrational number.

☛ Also Check:

Square Root of 256 - √256 = 16
Square Root of 40 - √40 = 6.32456
Square Root of 361 - √361 = 19
Square Root of 400 - √400 = 20
Square Root of 75 - √75 = 8.66025
Square Root of 19 - √19 = 4.35890
Square Root of 729 - √729 = 27

Square Root of 525 Solved Examples

Example 1: Solve the equation x² − 525 = 0

Solution:

x² - 525 = 0 i.e. x² = 525
x = ±√525
Since the value of the square root of 525 is 22.913,
⇒ x = +√525 or -√525 = 22.913 or -22.913.
Example 2: If the surface area of a cube is 3150 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 = 3150 in²
⇒ a = ±√525 in
Since length can't be negative,
⇒ a = √525
We know that the square root of 525 is 22.913.
⇒ a = 22.913 in
Example 3: If the surface area of a sphere is 2100π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 2100π in²
⇒ r = ±√525 in
Since radius can't be negative,
⇒ r = √525
The square root of 525 is 22.913.
⇒ r = 22.913 in

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FAQs on the Square Root of 525

What is the Value of the Square Root of 525?

The square root of 525 is 22.91287.

Why is the Square Root of 525 an Irrational Number?

Upon prime factorizing 525 i.e. 3¹ × 5² × 7¹, 3 is in odd power. Therefore, the square root of 525 is irrational.

What is the Square of the Square Root of 525?

The square of the square root of 525 is the number 525 itself i.e. (√525)² = (525)^2/2 = 525.

What is the Value of 7 square root 525?

The square root of 525 is 22.913. Therefore, 7 √525 = 7 × 22.913 = 160.390.

Is the number 525 a Perfect Square?

The prime factorization of 525 = 3¹ × 5² × 7¹. Here, the prime factor 3 is not in the pair. Therefore, 525 is not a perfect square.

If the Square Root of 525 is 22.913. Find the Value of the Square Root of 5.25.

Let us represent √5.25 in p/q form i.e. √(525/100) = 5.25/10 = 2.291. Hence, the value of √5.25 = 2.291

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