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Square Root of 1825

The square root of 1825 is expressed as √1825 in the radical form and as (1825)^½ or (1825)^0.5 in the exponent form. The square root of 1825 rounded up to 5 decimal places is 42.72002. It is the positive solution of the equation x² = 1825. We can express the square root of 1825 in its lowest radical form as 5 √73.

Square Root of 1825: 42.720018726587654
Square Root of 1825 in exponential form: (1825)^½ or (1825)^0.5
Square Root of 1825 in radical form: √1825 or 5 √73

Square Root of 1825

1.	What is the Square Root of 1825?
2.	How to find the Square Root of 1825?
3.	Is the Square Root of 1825 Irrational?
4.	FAQs

What is the Square Root of 1825?

The square root of 1825, (or root 1825), is the number which when multiplied by itself gives the product as 1825. Therefore, the square root of 1825 = √1825 = 5 √73 = 42.720018726587654.

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How to Find Square Root of 1825?

Square Root of 1825 by Long Division Method

Value of √1825 by Long Division Method

Explanation:

Forming pairs: 18 and 25
Find a number Y (4) such that whose square is <= 18. Now divide 18 by 4 with quotient as 4.
Bring down the next pair 25, to the right of the remainder 2. The new dividend is now 225.
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 2) such that 8Z × Z <= 225. After finding Z, together 8 and Z (2) form a new divisor 82 for the new dividend 225.
Divide 225 by 82 with the quotient as 2, giving the remainder = 225 - 82 × 2 = 225 - 164 = 61.
Now, let's find the decimal places after the quotient 42.
Bring down 00 to the right of this remainder 61. The new dividend is now 6100.
Add the last digit of quotient to divisor i.e. 2 + 82 = 84. To the right of 84, find a digit Z (which is 7) such that 84Z × Z <= 6100. Together they form a new divisor (847) for the new dividend (6100).
Divide 6100 by 847 with the quotient as 7, giving the remainder = 6100 - 847 × 7 = 6100 - 5929 = 171.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1825.

Therefore, the square root of 1825 by long division method is 42.7 approximately.

Is Square Root of 1825 Irrational?

The actual value of √1825 is undetermined. The value of √1825 up to 25 decimal places is 42.72001872658765583935824. Hence, the square root of 1825 is an irrational number.

☛ Also Check:

Square Root of 1000 - √1000 = 31.62278
Square Root of 22 - √22 = 4.69042
Square Root of 15 - √15 = 3.87298
Square Root of 36 - √36 = 6
Square Root of 56 - √56 = 7.48331
Square Root of 196 - √196 = 14
Square Root of 85 - √85 = 9.21954

Square Root of 1825 Solved Examples

Example 1: Solve the equation x² − 1825 = 0

Solution:

x² - 1825 = 0 i.e. x² = 1825
x = ±√1825
Since the value of the square root of 1825 is 42.720,
⇒ x = +√1825 or -√1825 = 42.720 or -42.720.
Example 2: If the area of an equilateral triangle is 1825√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 = 1825√3 in²
⇒ a = ±√7300 in
Since length can't be negative,
⇒ a = √7300 = 2 √1825
We know that the square root of 1825 is 42.720.
⇒ a = 85.440 in
Example 3: If the area of a circle is 1825π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 1825π in²
⇒ r = ±√1825 in
Since radius can't be negative,
⇒ r = √1825
The square root of 1825 is 42.720.
⇒ r = 42.720 in

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FAQs on the Square Root of 1825

What is the Value of the Square Root of 1825?

The square root of 1825 is 42.72001.

Why is the Square Root of 1825 an Irrational Number?

Upon prime factorizing 1825 i.e. 5² × 73¹, 73 is in odd power. Therefore, the square root of 1825 is irrational.

Is the number 1825 a Perfect Square?

The prime factorization of 1825 = 5² × 73¹. Here, the prime factor 73 is not in the pair. Therefore, 1825 is not a perfect square.

What is the Square of the Square Root of 1825?

The square of the square root of 1825 is the number 1825 itself i.e. (√1825)² = (1825)^2/2 = 1825.

What is the Square Root of 1825 in Simplest Radical Form?

We need to express 1825 as the product of its prime factors i.e. 1825 = 5 × 5 × 73. Therefore, √1825 = √5 × 5 × 73 = 5 √73. Thus, the square root of 1825 in the lowest radical form is 5 √73.

If the Square Root of 1825 is 42.720. Find the Value of the Square Root of 18.25.

Let us represent √18.25 in p/q form i.e. √(1825/100) = 18.25/10 = 4.272. Hence, the value of √18.25 = 4.272

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