72 is no a perfect square. It is represented as **√**72. The square source of 72 can only be simplified. In this mini-lesson we will discover to discover square root of 72 by long department method in addition to solved examples. Let us see what the square root of 72 is.

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**Square root of 72**:

**√**72 = 8.4852

**Square the 72: 722**= 5184

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

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

3. | How to uncover 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 find what is the number? It can be seen that there room no integers who square offers 72.

**√**72 = 8.4852

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

Any number which is either end or non-terminating and also has a repeating pattern in its decimal component is a rational number. We observed that **√**72 = 8.48528137423857. This decimal number is non-terminating and the decimal component has no repeating pattern. So it is no a reasonable number. Hence, **√**72 is an irrational number.

**Important Notes:**

**√**72 lies between

**√**64 and

**√**81, i.e.,

**√**72 lies between 8 and 9.Square root of a non-perfect square number in the most basic radical kind 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 discover the square root of any type of number. We can find the square source of 72 making use of long department method.**Click here to know much more about it.**

**Simplified Radical type 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 also 72. As soon as we discover the square source of any number, we take one number from each pair that the exact same numbers indigenous its element factorization and we main point them. The administer of 72 is 2 × 2 × 2 × 3 × 3 which has 1 pair of the same number. Thus, the simplest radical form of √**72 is 6**√**2.

### Square source 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, we pair turn off digits that a offered number starting with a number at one"s place. We placed a horizontal bar come indicate pairing.

**Step 2**:

**Now we need to discover a number i m sorry on squaring provides value less than or same to 72. As we know, 8 × 8 = 64**

**Step 3**:

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

**Step 4**: 4 is written at one"s place of brand-new divisor because when 164 is multiplied by 4, 656 is obtained which is less than 800. The derived answer currently is 144 and we bring down 00.

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

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

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

**Step 8**: 5 is written at one"s location of new divisor since when 16965 is multiplied by 8, 84825 is acquired which is much less than 89600. The derived answer currently is 4775 and we carry down 00.

So far we have gained **√**72 = 8.485. ~ above repeating this process further, us 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 of a circle having actually area 72π square inches equal to size of a square having area 72 square inches?

**Solution**

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

πr2 = 72π r2 = 72

By taking the square root on both sides, √r2= **√**72. We recognize that the square source of r2 is r.**The square root of 72 is 8.48 inches.See more: How Long Should I Shower After Tanning Bed, Your Skin Needs To Know!**

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

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

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