72 is not a perfect square. It is represented as **√**72. The square source of 72 deserve to only be simplified. In this mini-lesson we will discover to discover square source of 72 by long division method in addition to solved examples. Let us see what the square root of 72 is.

You are watching: Square root of 72 in radical form

**Square root of 72**:

**√**72 = 8.4852

**Square the 72: 722**= 5184

1. | What Is the Square source of 72? |

2. | Is Square source of 72 reasonable or Irrational? |

3. | How to uncover the Square source of 72? |

4. | FAQs ~ above Square source of 72 |

The initial number who square is 72 is the square root of 72. Deserve to you uncover what is that number? It can be watched that there space no integers who square offers 72.

**√**72 = 8.4852

To examine this answer, we can find (8.4852)2 and we deserve to see that we obtain a number 71.99861904. This number is an extremely close come 72 when the rounded to its nearest value.

Any number i beg your pardon is either terminating or non-terminating and also has a repeating pattern in the decimal part is a rational number. We observed that **√**72 = 8.48528137423857. This decimal number is non-terminating and also the decimal component has no repeating pattern. So that is not a rational number. Hence, **√**72 is an irrational number.

**Important Notes:**

**√**72 lies between

**√**64 and

**√**81, i.e.,

**√**72 lies between 8 and 9.Square source of a non-perfect square number in the easiest radical type can be uncovered using element factorization method. For example: 72 = 2 × 2 × 2 × 3 × 3. So,

**√**72 =

**√**(2 × 2 × 2 × 3 × 3) = 6

**√**2.

## How to find the Square root of 72?

There room different methods to find the square source of any kind of number. We can find the square root of 72 using long department method.**Click here to know an ext about it.**

**Simplified Radical kind of Square source of 72**

**72 is a composite number. Hence factors that 72 are 1, 2, 3, 4, 6, 8, 9 12, 18, 24, 36, and 72. Once we find the square root of any number, us take one number from every pair the the exact same numbers from its prime factorization and we multiply them. The administer of 72 is 2 × 2 × 2 × 3 × 3 which has 1 pair of the exact same number. Thus, the easiest radical type of √**72 is 6**√**2.

### Square source of 72 by Long department Method

The square root of 72 can be discovered using the long division as follows.

**Step 1**: In this step, we pair turn off digits the a provided number starting with a digit at one"s place. We put a horizontal bar come indicate pairing.

**Step 2**:

**Now we need to discover a number i beg your pardon on squaring offers value much less than or equal to 72. As we know, 8 × 8 = 64**

**Step 3**:

**Now, we have to carry down 00 and multiply the quotient through 2 which provides us 16.**

**Step 4**: 4 is written at one"s ar of brand-new divisor since when 164 is multiply by 4, 656 is acquired which is less than 800. The derived answer currently is 144 and we lug down 00.

**Step 5**: The quotient is now 84 and it is multiplied by 2. This gives 168, which climate would become the starting digit of the brand-new divisor.

**Step 6**: 7 is written at one"s ar of new divisor because when 1688 is multiply by 8, 13504 is acquired which is less than 14400. The acquired answer currently is 896 and we lug down 00.

**Step 7**: The quotient is now 848 and also it is multiply by 2. This gives 1696, which then would come to be the starting digit of the brand-new divisor.

**Step 8**: 5 is written at one"s place of new divisor due to the fact that when 16965 is multiplied by 8, 84825 is derived which is less than 89600. The obtained answer now is 4775 and we carry down 00.

So far we have obtained **√**72 = 8.485. ~ above repeating this process further, we get, **√**72 = 8.48528137423857

**Explore square roots making use of illustrations and also interactive examples.**

**Think Tank:**

**√**-72 and -

**√**72 same ?Is

**√**-72 a actual number?

**Example 2**: Is the radius the a circle having actually area 72π square inches equal to length of a square having area 72 square inches?

**Solution**

Radius is found using the formula the area that a one is πr2 square inches. Through the given information,

πr2 = 72π r2 = 72

By acquisition the square root on both sides, √r2= **√**72. We recognize that the square source of r2 is r.**The square source of 72 is 8.48 inches.See more: Convert 18 Mm Equals How Many Inches, Milimeter To Inches Conversion Chart**

**The size of square is found using the formula the area the square. Together per the given information,**

**Area = length × lengthThus, length = √**Area = **√**72 = 8.48 inches

Hence, radius of a circle having area 72π square inch is equal to the size of a square having area 72 square inches.