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Square Root of 2025

The square root of 2025 is expressed as √2025 in the radical form and as (2025)^½ or (2025)^0.5 in the exponent form. The square root of 2025 is 45. It is the positive solution of the equation x² = 2025. The number 2025 is a perfect square.

Square Root of 2025: 45
Square Root of 2025 in exponential form: (2025)^½ or (2025)^0.5
Square Root of 2025 in radical form: √2025

Square Root of 2025

1.	What is the Square Root of 2025?
2.	How to find the Square Root of 2025?
3.	Is the Square Root of 2025 Rational?
4.	FAQs

What is the Square Root of 2025?

The square root of 2025, (or root 2025), is the number which when multiplied by itself gives the product as 2025. Therefore, the square root of 2025 = √2025 = 45.

☛ Check: Square Root Calculator

How to Find Square Root of 2025?

Square Root of 2025 by Long Division Method

Value of √2025 by Long Division Method

Explanation:

Forming pairs: 20 and 25
Find a number Y (4) such that whose square is <= 20. Now divide 20 by 4 with quotient as 4.
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 (4) to the divisor (4) i.e. 4 + 4 = 8. To the right of 8, find a digit Z (which is 5) such that 8Z × Z <= 425. After finding Z, together 8 and Z (5) form a new divisor 85 for the new dividend 425.
Divide 425 by 85 with the quotient as 5, giving the remainder = 425 - 85 × 5 = 425 - 425 = 0.
We stop the process since the remainder is now 0 and there are no more digits that can be brought down.

Therefore, the square root of 2025 by long division method is 45.

Is Square Root of 2025 Rational?

The value of √2025 is 45. Hence, the square root of 2025 is a rational number.

☛ Also Check:

Square Root of 35 - √35 = 5.91608
Square Root of 17 - √17 = 4.12311
Square Root of 225 - √225 = 15
Square Root of 65 - √65 = 8.06226
Square Root of 14 - √14 = 3.74166
Square Root of 106 - √106 = 10.29563
Square Root of 256 - √256 = 16

Square Root of 2025 Solved Examples

Example 1: Solve the equation x² − 2025 = 0

Solution:

x² - 2025 = 0 i.e. x² = 2025
x = ±√2025
Since the value of the square root of 2025 is 45,
⇒ x = +√2025 or -√2025 = 45 or -45.
Example 2: If the area of an equilateral triangle is 2025√3 in². Find the length of one of the sides of the triangle.

Solution:

Let 'a' be the length of one of the sides of the equilateral triangle.
⇒ Area of the equilateral triangle = (√3/4)a² = 2025√3 in²
⇒ a = ±√8100 in
Since length can't be negative,
⇒ a = √8100 = 2 √2025
We know that the square root of 2025 is 45.
⇒ a = 90 in
Example 3: If the surface area of a sphere is 8100π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 8100π in²
⇒ r = ±√2025 in
Since radius can't be negative,
⇒ r = √2025
The square root of 2025 is 45.
⇒ r = 45 in

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FAQs on the Square Root of 2025

What is the Value of the Square Root of 2025?

The square root of 2025 is 45.

Why is the Square Root of 2025 a Rational Number?

Upon prime factorizing 2025 i.e. 3⁴ × 5², we find that all the prime factors are in even power. This implies that the square root of 2025 is a positive integer. Therefore, the square root of 2025 is rational.

Evaluate 9 plus 20 square root 2025

The given expression is 9 + 20 √2025. We know that the square root of 2025 is 45. Therefore, 9 + 20 √2025 = 9 + 20 × 45 = 9 + 900 = 909

If the Square Root of 2025 is 45. Find the Value of the Square Root of 20.25.

Let us represent √20.25 in p/q form i.e. √(2025/100) = 20.25/10 = 4. Hence, the value of √20.25 = 4

What is the Square of the Square Root of 2025?

The square of the square root of 2025 is the number 2025 itself i.e. (√2025)² = (2025)^2/2 = 2025.

What is the Square Root of -2025?

The square root of -2025 is an imaginary number. It can be written as √-2025 = √-1 × √2025 = i √2025 = 45i
where i = √-1 and it is called the imaginary unit.

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