The square root of 656 is expressed as √656 in the radical form and as (656)½ or (656)0.5 in the exponent form. The square root of 656 rounded up to 6 decimal places is 25.612497. It is the positive solution of the equation x2 = 656. We can express the square root of 656 in its lowest radical form as 4 √41.

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**Square Root of 656:**25.612496949731394

**Square Root of 656 in exponential form:**(656)½ or (656)0.5

**Square Root of 656 in radical form:**√656 or 4 √41

1. | What is the Square Root of 656? |

2. | How to find the Square Root of 656? |

3. | Is the Square Root of 656 Irrational? |

4. | FAQs |

The square root of 656, (or root 656), is the number which when multiplied by itself gives the product as 656. Therefore, the square root of 656 = √656 = 4 √41 = 25.612496949731394.

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### Value of √656 by Long Division Method

**Explanation:**

Therefore, the square root of 656 by long division method is 25.6 approximately.

The actual value of √656 is undetermined. The value of √656 up to 25 decimal places is 25.61249694973139474595287. Hence, the square root of 656 is an irrational number.

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**Example 1: Solve the equation x2 − 656 = 0**

**Solution:**

x2 - 656 = 0 i.e. x2 = 656x = ±√656Since the value of the square root of 656 is 25.612,⇒ x = +√656 or -√656 = 25.612 or -25.612.

**Example 2: If the area of a circle is 656π in2. Find the radius of the circle.**

**Solution:**

Let 'r' be the radius of the circle.⇒ Area of the circle = πr2 = 656π in2⇒ r = ±√656 inSince radius can't be negative,⇒ r = √656The square root of 656 is 25.612.⇒ r = 25.612 in

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## FAQs on the Square Root of 656

### What is the Value of the Square Root of 656?

The square root of 656 is 25.61249.

### Why is the Square Root of 656 an Irrational Number?

Upon prime factorizing 656 i.e. 24 × 411, 41 is in odd power. Therefore, the square root of 656 is irrational.

### If the Square Root of 656 is 25.612. Find the Value of the Square Root of 6.56.

Let us represent √6.56 in p/q form i.e. √(656/100) = 6.56/10 = 2.561. Hence, the value of √6.56 = 2.561

### What is the Square Root of 656 in Simplest Radical Form?

We need to express 656 as the product of its prime factors i.e. 656 = 2 × 2 × 2 × 2 × 41. Therefore, √656 = √2 × 2 × 2 × 2 × 41 = 4 √41. Thus, the square root of 656 in the lowest radical form is 4 √41.

### Is the number 656 a Perfect Square?

The prime factorization of 656 = 24 × 411. Here, the prime factor 41 is not in the pair. Therefore, 656 is not a perfect square.

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### What is the Square Root of -656?

The square root of -656 is an imaginary number. It can be written as √-656 = √-1 × √656 = i √656 = 25.612iwhere i = √-1 and it is called the imaginary unit.