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Square Root of 825

The square root of 825 is expressed as √825 in the radical form and as (825)^½ or (825)^0.5 in the exponent form. The square root of 825 rounded up to 9 decimal places is 28.722813233. It is the positive solution of the equation x² = 825. We can express the square root of 825 in its lowest radical form as 5 √33.

Square Root of 825: 28.722813232690143
Square Root of 825 in exponential form: (825)^½ or (825)^0.5
Square Root of 825 in radical form: √825 or 5 √33

Square Root of 825

1.	What is the Square Root of 825?
2.	How to find the Square Root of 825?
3.	Is the Square Root of 825 Irrational?
4.	FAQs

What is the Square Root of 825?

The square root of 825, (or root 825), is the number which when multiplied by itself gives the product as 825. Therefore, the square root of 825 = √825 = 5 √33 = 28.722813232690143.

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How to Find Square Root of 825?

Square Root of 825 by Long Division Method

Value of √825 by Long Division Method

Explanation:

Forming pairs: 08 and 25
Find a number Y (2) such that whose square is <= 8. Now divide 08 by 2 with quotient as 2.
Bring down the next pair 25, to the right of the remainder 4. The new dividend is now 425.
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 8) such that 4Z × Z <= 425. After finding Z, together 4 and Z (8) form a new divisor 48 for the new dividend 425.
Divide 425 by 48 with the quotient as 8, giving the remainder = 425 - 48 × 8 = 425 - 384 = 41.
Now, let's find the decimal places after the quotient 28.
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. 8 + 48 = 56. To the right of 56, find a digit Z (which is 7) such that 56Z × Z <= 4100. Together they form a new divisor (567) for the new dividend (4100).
Divide 4100 by 567 with the quotient as 7, giving the remainder = 4100 - 567 × 7 = 4100 - 3969 = 131.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 825.

Therefore, the square root of 825 by long division method is 28.7 approximately.

Is Square Root of 825 Irrational?

The actual value of √825 is undetermined. The value of √825 up to 25 decimal places is 28.72281323269014329925306. Hence, the square root of 825 is an irrational number.

☛ Also Check:

Square Root of 69 - √69 = 8.30662
Square Root of 29 - √29 = 5.38516
Square Root of 106 - √106 = 10.29563
Square Root of 140 - √140 = 11.83216
Square Root of 729 - √729 = 27
Square Root of 324 - √324 = 18
Square Root of 256 - √256 = 16

Square Root of 825 Solved Examples

Example 1: Solve the equation x² − 825 = 0

Solution:

x² - 825 = 0 i.e. x² = 825
x = ±√825
Since the value of the square root of 825 is 28.723,
⇒ x = +√825 or -√825 = 28.723 or -28.723.
Example 2: If the area of a circle is 825π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 825π in²
⇒ r = ±√825 in
Since radius can't be negative,
⇒ r = √825
The square root of 825 is 28.723.
⇒ r = 28.723 in
Example 3: If the surface area of a cube is 4950 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 = 4950 in²
⇒ a = ±√825 in
Since length can't be negative,
⇒ a = √825
We know that the square root of 825 is 28.723.
⇒ a = 28.723 in

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FAQs on the Square Root of 825

What is the Value of the Square Root of 825?

The square root of 825 is 28.72281.

Why is the Square Root of 825 an Irrational Number?

Upon prime factorizing 825 i.e. 3¹ × 5² × 11¹, 3 is in odd power. Therefore, the square root of 825 is irrational.

What is the Square Root of -825?

The square root of -825 is an imaginary number. It can be written as √-825 = √-1 × √825 = i √825 = 28.722i
where i = √-1 and it is called the imaginary unit.

What is the Square Root of 825 in Simplest Radical Form?

We need to express 825 as the product of its prime factors i.e. 825 = 3 × 5 × 5 × 11. Therefore, √825 = √3 × 5 × 5 × 11 = 5 √33. Thus, the square root of 825 in the lowest radical form is 5 √33.

What is the Value of 17 square root 825?

The square root of 825 is 28.723. Therefore, 17 √825 = 17 × 28.723 = 488.288.

What is the Square of the Square Root of 825?

The square of the square root of 825 is the number 825 itself i.e. (√825)² = (825)^2/2 = 825.

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