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Square Root of 1025

The square root of 1025 is expressed as √1025 in the radical form and as (1025)^½ or (1025)^0.5 in the exponent form. The square root of 1025 rounded up to 5 decimal places is 32.01562. It is the positive solution of the equation x² = 1025. We can express the square root of 1025 in its lowest radical form as 5 √41.

Square Root of 1025: 32.01562118716424
Square Root of 1025 in exponential form: (1025)^½ or (1025)^0.5
Square Root of 1025 in radical form: √1025 or 5 √41

Square Root of 1025

1.	What is the Square Root of 1025?
2.	How to find the Square Root of 1025?
3.	Is the Square Root of 1025 Irrational?
4.	FAQs

What is the Square Root of 1025?

The square root of 1025, (or root 1025), is the number which when multiplied by itself gives the product as 1025. Therefore, the square root of 1025 = √1025 = 5 √41 = 32.01562118716424.

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How to Find Square Root of 1025?

Square Root of 1025 by Long Division Method

Value of √1025 by Long Division Method

Explanation:

Forming pairs: 10 and 25
Find a number Y (3) such that whose square is <= 10. Now divide 10 by 3 with quotient as 3.
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 (3) to the divisor (3) i.e. 3 + 3 = 6. To the right of 6, find a digit Z (which is 2) such that 6Z × Z <= 125. After finding Z, together 6 and Z (2) form a new divisor 62 for the new dividend 125.
Divide 125 by 62 with the quotient as 2, giving the remainder = 125 - 62 × 2 = 125 - 124 = 1.
Now, let's find the decimal places after the quotient 32.
Bring down 00 to the right of this remainder 1. The new dividend is now 100.
Add the last digit of quotient to divisor i.e. 2 + 62 = 64. To the right of 64, find a digit Z (which is 0) such that 64Z × Z <= 100. Together they form a new divisor (640) for the new dividend (100).
Divide 100 by 640 with the quotient as 0, giving the remainder = 100 - 640 × 0 = 100 - 0 = 100.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1025.

Therefore, the square root of 1025 by long division method is 32.0 approx.

Is Square Root of 1025 Irrational?

The actual value of √1025 is undetermined. The value of √1025 up to 25 decimal places is 32.01562118716424343244109. Hence, the square root of 1025 is an irrational number.

☛ Also Check:

Square Root of 109 - √109 = 10.44031
Square Root of 42 - √42 = 6.48074
Square Root of 116 - √116 = 10.77033
Square Root of 25 - √25 = 5
Square Root of 200 - √200 = 14.14214
Square Root of 65 - √65 = 8.06226
Square Root of 10 - √10 = 3.16228

Square Root of 1025 Solved Examples

Example 1: Solve the equation x² − 1025 = 0

Solution:

x² - 1025 = 0 i.e. x² = 1025
x = ±√1025
Since the value of the square root of 1025 is 32.016,
⇒ x = +√1025 or -√1025 = 32.016 or -32.016.
Example 2: If the area of an equilateral triangle is 1025√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 = 1025√3 in²
⇒ a = ±√4100 in
Since length can't be negative,
⇒ a = √4100 = 2 √1025
We know that the square root of 1025 is 32.016.
⇒ a = 64.031 in
Example 3: If the surface area of a cube is 6150 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 = 6150 in²
⇒ a = ±√1025 in
Since length can't be negative,
⇒ a = √1025
We know that the square root of 1025 is 32.016.
⇒ a = 32.016 in

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FAQs on the Square Root of 1025

What is the Value of the Square Root of 1025?

The square root of 1025 is 32.01562.

Why is the Square Root of 1025 an Irrational Number?

Upon prime factorizing 1025 i.e. 5² × 41¹, 41 is in odd power. Therefore, the square root of 1025 is irrational.

Evaluate 10 plus 3 square root 1025

The given expression is 10 + 3 √1025. We know that the square root of 1025 is 32.016. Therefore, 10 + 3 √1025 = 10 + 3 × 32.016 = 10 + 96.047 = 106.047

What is the Square Root of -1025?

The square root of -1025 is an imaginary number. It can be written as √-1025 = √-1 × √1025 = i √1025 = 32.015i
where i = √-1 and it is called the imaginary unit.

What is the Square Root of 1025 in Simplest Radical Form?

We need to express 1025 as the product of its prime factors i.e. 1025 = 5 × 5 × 41. Therefore, √1025 = √5 × 5 × 41 = 5 √41. Thus, the square root of 1025 in the lowest radical form is 5 √41.

If the Square Root of 1025 is 32.016. Find the Value of the Square Root of 10.25.

Let us represent √10.25 in p/q form i.e. √(1025/100) = 10.25/10 = 3.202. Hence, the value of √10.25 = 3.202

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