Before we begin, let"s know the definition of square root. The symbol of square source is **√** and the is one integral component of mathematics. Once you know the basics of detect the square root of a number, you can solve any square root-related problem. In this quick lesson, we will learn around the square root the 65 and learn how to discover it using various methods like the long department method.

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Let us discover the square source of 65.

**Square source of 65**:

**√65**= 8.062

**Square that 65: 652**= 4225

1. | What Is the Square root of 65? |

2. | Is Square source of 65 Rational or Irrational? |

3. | How to uncover the Square source of 65? |

4. | Important note on Square source of 65 |

5. | Challenging concerns on Square root of 65 |

6. | FAQs ~ above Square root of 65 |

## What Is the Square source of 65?

The square root of a number is the number which, once multiplied by itself, gives the initial number as the product. The square root of 65 is 8.0622577483. The square root of 65 in the radical type is express as **√**65 and in the exponent form, it is expressed as 651/2. The square source of 65 rounded come 5 decimal places is 8.06225.

## Is the Square root of 65 Rational or Irrational?

Any number which cannot be expressed as p/q, where p and q are integers and q is no equal to 0, space called irrational numbers. Can **√**65 it is in expressed in together a way? In the decimal form, we can see the the decimal part of **√**65 is 8.0622577482986... which is non-terminating, non-repeating, and never-ending. Hence, **√**65 is one irrational number.

## How to find the Square root of 65?

65 is no a perfect square. Us can discover the square root of 65 by the approximation method. To find the accurate value, we have the right to use the long department method. In the approximation method, we find square numbers close come 65. We view that 64 and 81 space the perfect square number close to 65. The square root of 64 is 8 and the square root of 81 is 9. Therefore, the square root of 65 must lie between 8 and 9 and it must be closer to 8 as 65 is closer come 64. This an approach only offers us an approximate answer. To understand the exact value, we can use the long department method and find a much more accurate decimal worth for **√**65.

### Simplified Radical type of Square source of 65

**√**65 in the easiest radical form is **√**65 only. We cannot refer **√**65 as **√**(a×b), whereby a and b are integers. Thus, **√**65 is currently in the easiest radical form.

### Square root of 65 By Long Division

Let us follow these actions to discover the square root of 65 by long division.

**Step 1:**Set up the number in bag of 2 digits by place a bar over it, starting from the unit"s place.

**Step 2:**Find a divisor together that when we main point it come itself, the product is

**Step 3:**Since we do not have any kind of other digits after 65 to bring forward, we create pairs of zeros ~ the decimal point (as 65 = 65.000000...). Because we have added a decimal suggest in the dividend, let us encompass a decimal allude in the quotient ~ 8.

**Step 4:**Bring the 0 pair down and our brand-new dividend is 100. We need to uncover a new divisor. We dual the quotient 8 × 2 = 16 and find a new digit because that our units place for the brand-new divisor, such that the product of this new divisor v that number is less than or same to 100. Right here we will certainly place 0 as the units digit for our brand-new divisor and also place that after the decimal point in the quotient. Our brand-new divisor is 160.

**Step 5:**We lug down the following pair the zeros and our new dividend is 10000. We require to find a new divisor like exactly how we go in the ahead step. We double the quotient 8 × 2 = 16 and also find the units place of our brand-new divisor such that the product is much less than or equal to 10000. We see that 1606 × 6 = 9636 i beg your pardon is close to 10000. Thus, we location 6 at the units location of our new divisor and place 6 in the quotient.

Bring the following pair the zeros down. We will certainly repeat the procedure to uncover the next decimal place. The square source of 65 approximately 2 decimal places is 8.06 as shown above. Deserve to you proceed the process and discover the square root of 65 to 5 decimal places?

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**Important Notes:**

**√**65.In the exponent form, the square source of 65 is expressed as 651/2.The actual roots of

**√**65 are 8.0622577.

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**Challenging Questions:**

**√**

**√**65?Determine the square root of 655 by the long division method.