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Square Root of 725

The square root of 725 is expressed as √725 in the radical form and as (725)^½ or (725)^0.5 in the exponent form. The square root of 725 rounded up to 7 decimal places is 26.9258240. It is the positive solution of the equation x² = 725. We can express the square root of 725 in its lowest radical form as 5 √29.

Square Root of 725: 26.92582403567252
Square Root of 725 in exponential form: (725)^½ or (725)^0.5
Square Root of 725 in radical form: √725 or 5 √29

Square Root of 725

1.	What is the Square Root of 725?
2.	How to find the Square Root of 725?
3.	Is the Square Root of 725 Irrational?
4.	FAQs

What is the Square Root of 725?

The square root of 725, (or root 725), is the number which when multiplied by itself gives the product as 725. Therefore, the square root of 725 = √725 = 5 √29 = 26.92582403567252.

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How to Find Square Root of 725?

Square Root of 725 by Long Division Method

Value of √725 by Long Division Method

Explanation:

Forming pairs: 07 and 25
Find a number Y (2) such that whose square is <= 7. Now divide 07 by 2 with quotient as 2.
Bring down the next pair 25, to the right of the remainder 3. The new dividend is now 325.
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 6) such that 4Z × Z <= 325. After finding Z, together 4 and Z (6) form a new divisor 46 for the new dividend 325.
Divide 325 by 46 with the quotient as 6, giving the remainder = 325 - 46 × 6 = 325 - 276 = 49.
Now, let's find the decimal places after the quotient 26.
Bring down 00 to the right of this remainder 49. The new dividend is now 4900.
Add the last digit of quotient to divisor i.e. 6 + 46 = 52. To the right of 52, find a digit Z (which is 9) such that 52Z × Z <= 4900. Together they form a new divisor (529) for the new dividend (4900).
Divide 4900 by 529 with the quotient as 9, giving the remainder = 4900 - 529 × 9 = 4900 - 4761 = 139.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 725.

Therefore, the square root of 725 by long division method is 26.9 approximately.

Is Square Root of 725 Irrational?

The actual value of √725 is undetermined. The value of √725 up to 25 decimal places is 26.92582403567252015625355. Hence, the square root of 725 is an irrational number.

☛ Also Check:

Square Root of 240 - √240 = 15.49193
Square Root of 2 - √2 = 1.41421
Square Root of 29 - √29 = 5.38516
Square Root of 900 - √900 = 30
Square Root of 74 - √74 = 8.60233
Square Root of 97 - √97 = 9.84886
Square Root of 40 - √40 = 6.32456

Square Root of 725 Solved Examples

Example 1: Solve the equation x² − 725 = 0

Solution:

x² - 725 = 0 i.e. x² = 725
x = ±√725
Since the value of the square root of 725 is 26.926,
⇒ x = +√725 or -√725 = 26.926 or -26.926.
Example 2: If the surface area of a sphere is 2900π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 2900π in²
⇒ r = ±√725 in
Since radius can't be negative,
⇒ r = √725
The square root of 725 is 26.926.
⇒ r = 26.926 in
Example 3: If the area of a circle is 725π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 725π in²
⇒ r = ±√725 in
Since radius can't be negative,
⇒ r = √725
The square root of 725 is 26.926.
⇒ r = 26.926 in

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FAQs on the Square Root of 725

What is the Value of the Square Root of 725?

The square root of 725 is 26.92582.

Why is the Square Root of 725 an Irrational Number?

Upon prime factorizing 725 i.e. 5² × 29¹, 29 is in odd power. Therefore, the square root of 725 is irrational.

Evaluate 2 plus 11 square root 725

The given expression is 2 + 11 √725. We know that the square root of 725 is 26.926. Therefore, 2 + 11 √725 = 2 + 11 × 26.926 = 2 + 296.184 = 298.184

What is the Square Root of 725 in Simplest Radical Form?

We need to express 725 as the product of its prime factors i.e. 725 = 5 × 5 × 29. Therefore, √725 = √5 × 5 × 29 = 5 √29. Thus, the square root of 725 in the lowest radical form is 5 √29.

Is the number 725 a Perfect Square?

The prime factorization of 725 = 5² × 29¹. Here, the prime factor 29 is not in the pair. Therefore, 725 is not a perfect square.

What is the Square of the Square Root of 725?

The square of the square root of 725 is the number 725 itself i.e. (√725)² = (725)^2/2 = 725.

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