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 division method in addition to solved examples. Let united state see what the square source of 72 is.

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Square source of 7272 = 8.4852Square the 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 ~ above Square root of 72

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

72 = 8.4852

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

Any number i m sorry is either end or non-terminating and also has a repeating pattern in that decimal component 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 it is not a rational number. Hence, 72 is an irrational number.

Important Notes:

72 lies between 64 and 81. Hence, 72 lies between 64 and 81, i.e., 72 lies in between 8 and 9.Square root of a non-perfect square number in the easiest radical type can be discovered using element factorization method. For example: 72 = 2 × 2 × 2 × 3 × 3. So, 72 = (2 × 2 × 2 × 3 × 3) = 62.

## How to discover the Square source of 72?

There space different methods to discover the square root of any type of number. We can find the square root of 72 making use of long division method.Click here to know much more about it.

### Simplified Radical kind 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 72. As soon as we uncover the square root of any type of number, we take one number from each pair that the exact same numbers indigenous its prime factorization and also we multiply them. The administrate of 72 is 2 × 2 × 2 × 3 × 3 which has actually 1 pair of the same number. Thus, the simplest radical kind of √72 is 62.

### Square source of 72 by Long division Method

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

Step 1: In this step, us pair turn off digits of 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 m sorry on squaring gives value much less than or equal to 72. Together we know, 8 × 8 = 64 Step 3: Now, we have actually to bring down 00 and multiply the quotient by 2 which offers us 16. Step 4: 4 is written at one"s place of new divisor because when 164 is multiply by 4, 656 is acquired which is much less than 800. The obtained answer now 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 come to be 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 derived which is much less than 14400. The acquired answer currently is 896 and also we carry down 00.Step 7: The quotient is now 848 and it is multiply by 2. This gives 1696, which then would become the starting digit that the brand-new divisor.Step 8: 5 is written at one"s ar 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 currently is 4775 and we carry down 00.

So much we have got 72 = 8.485. ~ above repeating this procedure further, us get, 72 = 8.48528137423857

Explore square roots using illustrations and interactive examples.

Think Tank:

Are -72 and -72 same ?Is -72 a real number?

Example 2: Is the radius that 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 of area the a one is πr2 square inches. By the provided information,

πr2 = 72π r2 = 72

By taking 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.

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The length of square is found using the formula that area that square. As per the provided information,

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

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