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

You are watching: What is the square root of 72 simplified

**Square root of 72**:

**√**72 = 8.4852

**Square of 72: 722**= 5184

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

2. | Is Square root of 72 rational or Irrational? |

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

4. | FAQs ~ above Square root of 72 |

The initial number who square is 72 is the square root of 72. Can you uncover what is the number? It can be seen that there are no integers whose square gives 72.

**√**72 = 8.4852

To inspect this answer, us can find (8.4852)2 and we deserve to see that we get a number 71.99861904. This number is really close to 72 when its rounded come its nearest value.

Any number i m sorry is either terminating or non-terminating and also has a repeating pattern in that is decimal part is a rational number. We observed that **√**72 = 8.48528137423857. This decimal number is non-terminating and the decimal part has no repeating pattern. So the is no a reasonable number. Hence, **√**72 is an irrational number.

**Important Notes:**

**√**72 lies in between

**√**64 and

**√**81, i.e.,

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

**√**72 =

**√**(2 × 2 × 2 × 3 × 3) = 6

**√**2.

## How to uncover the Square source of 72?

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

**Simplified Radical type of Square root of 72**

**72 is a composite number. Hence factors of 72 are 1, 2, 3, 4, 6, 8, 9 12, 18, 24, 36, and also 72. Once we find the square source of any type of number, we take one number from every pair that the exact same numbers from its element factorization and also we multiply them. The administrate of 72 is 2 × 2 × 2 × 3 × 3 which has actually 1 pair of the exact same number. Thus, the most basic radical form of √**72 is 6**√**2.

### Square root of 72 by Long division Method

The square source of 72 can be found using the long department as follows.

**Step 1**: In this step, us pair off digits that a given number starting with a digit at one\"s place. We placed a horizontal bar come indicate pairing.

**Step 2**:

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

**Step 3**:

**Now, we have actually to carry down 00 and multiply the quotient by 2 which offers us 16.**

**Step 4**: 4 is written at one\"s location of new divisor since when 164 is multiplied by 4, 656 is obtained which is less than 800. The acquired answer currently is 144 and we carry down 00.

**Step 5**: The quotient is now 84 and it is multiply by 2. This gives 168, which climate would end up being the beginning digit of the new divisor.

**Step 6**: 7 is written at one\"s place of brand-new divisor since when 1688 is multiplied by 8, 13504 is acquired which is less than 14400. The obtained answer now is 896 and also we lug down 00.

**Step 7**: The quotient is currently 848 and it is multiply by 2. This gives 1696, which climate would become the starting digit the the brand-new divisor.

**Step 8**: 5 is written at one\"s ar of new divisor because when 16965 is multiplied by 8, 84825 is obtained which is much less than 89600. The derived answer currently is 4775 and we bring down 00.

So much we have acquired **√**72 = 8.485. Top top 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 that a circle having actually area 72π square inches same to size of a square having area 72 square inches?

**Solution**

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

πr2 = 72π r2 = 72

By acquisition the square root on both sides, √r2= **√**72. We understand that the square source of r2 is r.**The square source of 72 is 8.48 inches.See more: What Mission Does Soap Die In Mw3, Soap Mactavish**

**The size of square is discovered using the formula of area of square. Together per the offered information,**

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

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