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

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**Square source of 72**:

**√**72 = 8.4852

**Square that 72: 722**= 5184

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

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

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

4. | FAQs top top Square source of 72 |

The original number whose square is 72 is the square root of 72. Can you uncover what is the number? It can be viewed that there space no integers who square offers 72.

**√**72 = 8.4852

To check this answer, us can discover (8.4852)2 and we deserve to see that we gain a number 71.99861904. This number is very close to 72 when that is rounded come its nearest value.

Any number i beg your pardon is either end or non-terminating and has a repeating pattern in that decimal component is a rational number. We experienced that **√**72 = 8.48528137423857. This decimal number is non-terminating and the decimal part has no repeating pattern. So the is not a reasonable number. Hence, **√**72 is one 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 most basic radical kind can be found using element factorization method. Because that 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 are different methods to uncover the square root of any kind of number. We can find the square source of 72 utilizing long division method.**Click here to know more about it.**

**Simplified Radical type of Square source of 72**

**72 is a composite number. Hence factors the 72 are 1, 2, 3, 4, 6, 8, 9 12, 18, 24, 36, and also 72. As soon as we find the square source of any number, we take one number from each pair the the same numbers from its element factorization and we multiply them. The factorization of 72 is 2 × 2 × 2 × 3 × 3 which has 1 pair of the exact same number. Thus, the easiest radical kind of √**72 is 6**√**2.

### Square source of 72 by Long division Method

The square root of 72 can be uncovered using the long department as follows.

**Step 1**: In this step, we pair off digits that a given number beginning with a number at one"s place. We put a horizontal bar to indicate pairing.

**Step 2**:

**Now we require to find a number which on squaring provides value less than or same to 72. Together we know, 8 × 8 = 64**

**Step 3**:

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

**Step 4**: 4 is written at one"s ar of brand-new divisor because when 164 is multiply by 4, 656 is obtained which is less than 800. The derived answer now 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 become the starting digit that the brand-new divisor.

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

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

**Step 8**: 5 is written at one"s place of brand-new divisor since when 16965 is multiplied by 8, 84825 is obtained which is much less than 89600. The acquired answer now is 4775 and we bring down 00.

So much we have gained **√**72 = 8.485. On repeating this process further, we get, **√**72 = 8.48528137423857

**Explore square roots using illustrations and interactive examples.**

**Think Tank:**

**√**-72 and -

**√**72 same ?Is

**√**-72 a actual number?

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

**Solution**

Radius is found using the formula the area that a circle is πr2 square inches. By the offered information,

πr2 = 72π r2 = 72

By acquisition the square source on both sides, √r2= **√**72. We understand that the square source of r2 is r.**The square root of 72 is 8.48 inches.See more: Where Is The Transmission Control Module Located ? Where Is The Transmission Control Module Located**

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

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

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