Before us begin, let"s know the meaning of square root. The prize of square root is **√** and that is one integral part of mathematics. Once you recognize the basics of finding the square source of a number, you deserve to solve any square root-related problem. In this short lesson, we will learn around the square root the 65 and also learn exactly how to uncover it using various methods like the long department method.

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Let us find the square source of 65.

**Square source of 65**:

**√65**= 8.062

**Square of 65: 652**= 4225

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

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

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

4. | Important notes on Square root of 65 |

5. | Challenging questions on Square source of 65 |

6. | FAQs on Square root of 65 |

## What Is the Square root of 65?

The square root of a number is the number which, as soon as multiplied by itself, gives the initial number together the product. The square root of 65 is 8.0622577483. The square root of 65 in the radical type is express as **√**65 and also in the exponent form, that is expressed together 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 together p/q, where p and also q are integers and q is not equal come 0, are called irrational numbers. Can **√**65 it is in expressed in such a way? In the decimal form, we can see that the decimal component of **√**65 is 8.0622577482986... which is non-terminating, non-repeating, and never-ending. Hence, **√**65 is one irrational number.

## How to uncover the Square root of 65?

65 is no a perfect square. We can discover the square root of 65 by the approximation method. To find the accurate value, we can use the long division method. In the approximation method, we find square number close come 65. We check out that 64 and also 81 are the perfect square number close to 65. The square source of 64 is 8 and also the square root of 81 is 9. Therefore, the square root of 65 should lie between 8 and also 9 and it must be closer to 8 together 65 is closer come 64. This an approach only gives us an approximate answer. To understand the specific value, we can use the long division method and find a more accurate decimal worth for **√**65.

### Simplified Radical form of Square source of 65

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

### Square source of 65 By Long Division

Let us follow these steps to find the square source of 65 by lengthy division.

**Step 1:**Set increase the number in pairs of two digits by placing a bar over it, starting from the unit"s place.

**Step 2:**Find a divisor together that when we multiply it to itself, the product is

**Step 3:**Since we carry out not have any type of other number after 65 to carry forward, we write pairs of zeros after the decimal allude (as 65 = 65.000000...). Due to the fact that we have added a decimal allude in the dividend, let us include a decimal allude in the quotient ~ 8.

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

**Step 5:**We lug down the next pair that zeros and our new dividend is 10000. We need to discover a brand-new divisor like just how we go in the ahead step. We dual the quotient 8 × 2 = 16 and find the units place of our new divisor such the the product is less than or same to 10000. We check out that 1606 × 6 = 9636 which is close come 10000. Thus, we place 6 in ~ the units ar of our brand-new divisor and place 6 in the quotient.

Bring the following pair of zeros down. We will repeat the process to uncover the next decimal place. The square source of 65 approximately 2 decimal places is 8.06 as shown above. Can you continue the process and find the square root of 65 come 5 decimal places?

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**Important Notes:**

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

**√**65 are 8.0622577.

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**Challenging Questions:**

**√**

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