72 is not a perfect square. It is represented as **√**72. The square root of 72 deserve to just be streamlined. In this mini-lesboy we will learn to find square root of 72 by lengthy department strategy along with fixed examples. Let us see what the square root of 72 is.

You are watching: What is the square root of 24

**Square Root of 72**:

**√**72 = 8.4852

**Square of 72: 722**= 5184

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

2. | Is Square Root of 72 Rational or Irrational? |

3. | How to Find the Square Root of 72? |

4. | FAQs on Square Root of 72 |

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

**√**72 = 8.4852

To inspect this answer, we have the right to uncover (8.4852)2 and also we can check out that we gain a number 71.99861904. This number is incredibly close to 72 as soon as its rounded to its nearemainder value.

Any number which is either terminating or non-terminating and also has actually 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 part has actually no repeating pattern. So it is NOT a rational number. Hence, **√**72 is an irrational number.

**Important Notes:**

**√**72 lies in between

**√**64 and

**√**81, i.e.,

**√**72 lies between 8 and also 9.Square root of a non-perfect square number in the most basic radical form deserve to be found utilizing prime 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?

Tright here are different approaches to uncover the square root of any type of number. We can find the square root of 72 using lengthy division strategy.**Click here to recognize more around it.**

**Simplified Radical Form 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 72. When we find the square root of any type of number, we take one number from each pair of the exact same numbers from its prime factorization and also we multiply them. The factorization of 72 is 2 × 2 × 2 × 3 × 3 which has 1 pair of the very same number. Therefore, the easiest radical create of √**72 is 6**√**2.

### Square Root of 72 by Long Division Method

The square root of 72 can be discovered utilizing the long department as follows.

**Step 1**: In this action, we pair off digits of a given number founding via a digit at one"s location. We put a horizontal bar to indicate pairing.

**Step 2**:

**Now we should discover a number which on squaring gives worth much less than or equal to 72. As we know, 8 × 8 = 64**

**Tip 3**:

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

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

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

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

**Tip 7**: The quotient is currently 848 and also it is multiplied by 2. This offers 1696, which then would certainly become the starting digit of the brand-new divisor.

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

So far we have gained **√**72 = 8.485. On repeating this process even more, we acquire, **√**72 = 8.48528137423857

**Explore square roots utilizing illustrations and also interactive examples.**

**Think Tank:**

**√**-72 and -

**√**72 exact same ?Is

**√**-72 a genuine 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 utilizing the formula of location of a circle is πr2 square inches. By the provided indevelopment,

πr2 = 72π r2 = 72

By taking the square root on both sides, √r2= **√**72. We recognize that the square root of r2 is r.**The square root of 72 is 8.48 inches.See more: Calculate The Concentration Of H+ Ions In A 0.010 M Aqueous Solution Of Sulfuric Acid.**

**The length of square is uncovered using the formula of area of square. As per the provided indevelopment,**

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

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