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:**26.92582403567252

**Square Root of 725 in exponential form:**(725)½ or (725)0.5

**Square Root of 725 in radical form:**√725 or 5 √29

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:**

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.