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.

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

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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

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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Value of √725 by Long Division Method

Explanation:

Forming pairs: 07 and 25Find a number Y (2) such that whose square is 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 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 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.


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Example 1: Solve the equation x2 − 725 = 0

Solution:

x2 - 725 = 0 i.e. x2 = 725x = ±√725Since the value of the square root of 725 is 26.926,⇒ x = +√725 or -√725 = 26.926 or -26.926.


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 inSince radius can't be negative,⇒ r = √725The 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.

See more: A Device That Converts Electrical Energy Into Mechanical Energy

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.