The square root of 260 is expressed as √260 in the radical form and as (260)½ or (260)0.5 in the exponent form. The square root of 260 rounded up to 8 decimal places is 16.12451550. It is the positive solution of the equation x2 = 260. We can express the square root of 260 in its lowest radical form as 2 √65.

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**Square Root of 260:**16.1245154965971

**Square Root of 260 in exponential form:**(260)½ or (260)0.5

**Square Root of 260 in radical form:**√260 or 2 √65

1. | What Is the Square Root of 260? |

2. | Is Square Root of 260 Rational or Irrational? |

3. | How to Find the Square Root of 260? |

4. | Important Notes on Square Root of 260 |

5. | FAQs on Square Root of 260 |

The square root of 260 in decimal form is = 16.1245The square root of 260 can be written as √260 and (260)1/2

## Is Square Root of 260 Rational or Irrational?

The square root of 260 is a non-terminating and non-repeating numberTherefore, the square root of 260 is an irrational number because it cannot be expressed in the form of p/q where q ≠ 0.

Now we will calculate the square root of 260 using the following methods

### Square Root of 260 Using Prime Factorization Method

The prime factors of 260 in pairs: (2 × 2) × 5 × 13Now, the square root of 260: √260 = √((2 × 2) × 5 × 13)So, the square root of 260 = 2 × √(5 × 13) = 2√65### Square Root of 260 By Long Division

Start Grouping the digits from the unit’s place in pairs of two by drawing a line on top of them. We get two pairs in this case (2 & 60).Find a number(n) which when multiplied with itself n × n ≤ 2. So, n will be 1 as 1 × 1 = 1.Bring down the pair of 60. So, our new dividend is 160. Now find a number(m) such that 2m × m ≤ 160. The number m will be 6 as 26 × 6 = 156 ≤ 160. Therefore, the remainder is 4.Add a decimal in the dividend and quotient part simultaneously. Also, add 3 pairs of zero in the dividend part (260. 00 00 00) and repeat the above step for all the pairs of zero.So, we get the square root of √260 = 16.124 by the long division method.

Explore square roots using illustrations and interactive examples

The number 260 is not a perfect square.The square root of 260 is an irrational number.The square root of -260 is an imaginary number.

**Example 1:**Mario wants to find out the square root of -260. Can you help Mario?

**Solution:**The square root of negative numbers is imaginary numbers.Because the square of any number (positive or negative) will result in a positive number.So, the square of -260 is written as √-260 = ±16.1245i. (where i = √-1)

**Example 2:**Find the square root of 260 using the repeated subtraction method?

**Solution:**

Hence, the square root of 260 via the approximation method is 16.12

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## FAQs on the Square Root of 260

### What is the Value of the Square Root of 260?

The square root of 260 is 16.12451.

### Why is the Square Root of 260 an Irrational Number?

Upon prime factorizing 260 i.e. 22 × 51 × 131, 5 is in odd power. Therefore, the square root of 260 is irrational.

### What is the Square of the Square Root of 260?

The square of the square root of 260 is the number 260 itself i.e. (√260)2 = (260)2/2 = 260.

### What is the Square Root of 260 in Simplest Radical Form?

We need to express 260 as the product of its prime factors i.e. 260 = 2 × 2 × 5 × 13. Therefore, √260 = √2 × 2 × 5 × 13 = 2 √65. Thus, the square root of 260 in the lowest radical form is 2 √65.

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### Evaluate 18 plus 16 square root 260

The given expression is 18 + 16 √260. We know that the square root of 260 is 16.125. Therefore, 18 + 16 √260 = 18 + 16 × 16.125 = 18 + 257.992 = 275.992

### What is the Value of 4 square root 260?

The square root of 260 is 16.125. Therefore, 4 √260 = 4 × 16.125 = 64.498.