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Square Root of 925

The square root of 925 is expressed as √925 in the radical form and as (925)^½ or (925)^0.5 in the exponent form. The square root of 925 rounded up to 7 decimal places is 30.4138127. It is the positive solution of the equation x² = 925. We can express the square root of 925 in its lowest radical form as 5 √37.

Square Root of 925: 30.4138126514911
Square Root of 925 in exponential form: (925)^½ or (925)^0.5
Square Root of 925 in radical form: √925 or 5 √37

Square Root of 925

1.	What is the Square Root of 925?
2.	How to find the Square Root of 925?
3.	Is the Square Root of 925 Irrational?
4.	FAQs

What is the Square Root of 925?

The square root of 925, (or root 925), is the number which when multiplied by itself gives the product as 925. Therefore, the square root of 925 = √925 = 5 √37 = 30.4138126514911.

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How to Find Square Root of 925?

Square Root of 925 by Long Division Method

Value of √925 by Long Division Method

Explanation:

Forming pairs: 09 and 25
Find a number Y (3) such that whose square is <= 9. Now divide 09 by 3 with quotient as 3.
Bring down the next pair 25, to the right of the remainder 0. The new dividend is now 25.
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 0) such that 6Z × Z <= 25. After finding Z, together 6 and Z (0) form a new divisor 60 for the new dividend 25.
Divide 25 by 60 with the quotient as 0, giving the remainder = 25 - 60 × 0 = 25 - 0 = 25.
Now, let's find the decimal places after the quotient 30.
Bring down 00 to the right of this remainder 25. The new dividend is now 2500.
Add the last digit of quotient to divisor i.e. 0 + 60 = 60. To the right of 60, find a digit Z (which is 4) such that 60Z × Z <= 2500. Together they form a new divisor (604) for the new dividend (2500).
Divide 2500 by 604 with the quotient as 4, giving the remainder = 2500 - 604 × 4 = 2500 - 2416 = 84.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 925.

Therefore, the square root of 925 by long division method is 30.4 approximately.

Is Square Root of 925 Irrational?

The actual value of √925 is undetermined. The value of √925 up to 25 decimal places is 30.41381265149109844499842. Hence, the square root of 925 is an irrational number.

☛ Also Check:

Square Root of 23 - √23 = 4.79583
Square Root of 1521 - √1521 = 39
Square Root of 54 - √54 = 7.34847
Square Root of 288 - √288 = 16.97056
Square Root of 400 - √400 = 20
Square Root of 34 - √34 = 5.83095
Square Root of 784 - √784 = 28

Square Root of 925 Solved Examples

Example 1: Solve the equation x² − 925 = 0

Solution:

x² - 925 = 0 i.e. x² = 925
x = ±√925
Since the value of the square root of 925 is 30.414,
⇒ x = +√925 or -√925 = 30.414 or -30.414.
Example 2: If the surface area of a sphere is 3700π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 3700π in²
⇒ r = ±√925 in
Since radius can't be negative,
⇒ r = √925
The square root of 925 is 30.414.
⇒ r = 30.414 in
Example 3: If the area of an equilateral triangle is 925√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 = 925√3 in²
⇒ a = ±√3700 in
Since length can't be negative,
⇒ a = √3700 = 2 √925
We know that the square root of 925 is 30.414.
⇒ a = 60.828 in

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FAQs on the Square Root of 925

What is the Value of the Square Root of 925?

The square root of 925 is 30.41381.

Why is the Square Root of 925 an Irrational Number?

Upon prime factorizing 925 i.e. 5² × 37¹, 37 is in odd power. Therefore, the square root of 925 is irrational.

What is the Square Root of 925 in Simplest Radical Form?

We need to express 925 as the product of its prime factors i.e. 925 = 5 × 5 × 37. Therefore, √925 = √5 × 5 × 37 = 5 √37. Thus, the square root of 925 in the lowest radical form is 5 √37.

If the Square Root of 925 is 30.414. Find the Value of the Square Root of 9.25.

Let us represent √9.25 in p/q form i.e. √(925/100) = 9.25/10 = 3.041. Hence, the value of √9.25 = 3.041

What is the Value of 18 square root 925?

The square root of 925 is 30.414. Therefore, 18 √925 = 18 × 30.414 = 547.449.

Is the number 925 a Perfect Square?

The prime factorization of 925 = 5² × 37¹. Here, the prime factor 37 is not in the pair. Therefore, 925 is not a perfect square.

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