72 is no a perfect square. It is stood for as 72. The square root of 72 deserve to 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.

You are watching: All real square roots of 100

Square root of 7272 = 8.4852Square the 72: 722 = 5184
1.What Is the Square source of 72?
2.Is Square root of 72 reasonable or Irrational?
3.How to discover the Square source of 72?
4.FAQs on Square root of 72

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

72 = 8.4852

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

Any number i m sorry is either terminating or non-terminating and also has a repeating pattern in the 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 not a reasonable number. Hence, 72 is an irrational number.

Important Notes:

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

How to find the Square root of 72?

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

Simplified Radical kind of Square source 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. As soon as we uncover the square source of any kind of number, us take one number from each pair of the very same numbers native its prime factorization and also we multiply them. The factorization of 72 is 2 × 2 × 2 × 3 × 3 which has 1 pair of the same number. Thus, the simplest radical form of √72 is 62.

Square source of 72 by Long department Method

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

Step 1: In this step, we pair turn off digits of a offered number starting with a digit at one"s place. We placed a horizontal bar come indicate pairing.Step 2: Now we need to uncover a number which on squaring offers value less than or equal to 72. As we know, 8 × 8 = 64 Step 3: Now, we have actually to lug 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 since when 164 is multiply by 4, 656 is derived which is less than 800. The derived answer currently is 144 and we carry 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 starting digit that the new divisor.Step 6: 7 is written at one"s ar of new divisor because when 1688 is multiplied by 8, 13504 is acquired which is less than 14400. The acquired answer now is 896 and also we carry down 00.Step 7: The quotient is now 848 and also it is multiply by 2. This gives 1696, which then would end up being the starting digit the the brand-new divisor.Step 8: 5 is written at one"s place of brand-new divisor because when 16965 is multiplied by 8, 84825 is acquired which is much less than 89600. The obtained answer now is 4775 and we bring down 00.


So much we have gained 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:

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? 


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

πr2 = 72π r2 = 72

By acquisition the square source on both sides, √r2= 72. We recognize that the square root of r2 is r.The square source of 72 is 8.48 inches.

See more: Used 2006 Ford Fusion Gas Tank Size, Reserve Tank Size

The size of square is uncovered using the formula of area the square. As per the provided information,

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

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