72 is no a perfect square. It is represented as 72. The square root of 72 can only it is in simplified. In this mini-lesson us will find out to find square root of 72 by long division method along with solved examples. Let us see what the square root of 72 is.

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

The initial number who square is 72 is the square root of 72. Can you discover what is that number? It can be viewed that there are no integers whose square gives 72.

72 = 8.4852

To examine this answer, we can find (8.4852)2 and we have the right to see that we gain a number 71.99861904. This number is really close come 72 when the rounded to its nearest value.

Any number which is either end or non-terminating and has a repeating pattern in its decimal part is a rational number. We witnessed that 72 = 8.48528137423857. This decimal number is non-terminating and the decimal part has no repeating pattern. So it is no a reasonable number. Hence, 72 is one irrational number.

Important Notes:

72 lies in between 64 and 81. Hence, 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 type can be discovered using element factorization method. Because that example: 72 = 2 × 2 × 2 × 3 × 3. So, 72 = (2 × 2 × 2 × 3 × 3) = 62.

How to find the Square root of 72?

There are different methods to discover the square root of any kind of number. Us can find the square source of 72 using long department method.Click here to know more about it.

Simplified Radical type 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. As soon as we uncover the square source of any number, us take one number from every pair the the very same numbers indigenous its prime factorization and we main point them. The administer of 72 is 2 × 2 × 2 × 3 × 3 which has 1 pair of the exact same number. Thus, the easiest radical form of √72 is 62.

Square source of 72 by Long division Method

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

Step 1: In this step, us pair turn off digits of a provided number beginning with a digit at one"s place. We placed a horizontal bar come indicate pairing.Step 2: Now we require to find a number i beg your pardon on squaring offers value much less than or same to 72. Together we know, 8 × 8 = 64 Step 3: Now, we have actually to lug down 00 and also multiply the quotient through 2 which gives us 16. Step 4: 4 is written at one"s ar of brand-new divisor since when 164 is multiply by 4, 656 is derived which is less than 800. The acquired answer currently is 144 and we lug down 00.Step 5: The quotient is currently 84 and it is multiply by 2. This gives 168, which climate would end up being the starting digit of the new divisor.Step 6: 7 is written at one"s place of new divisor due to the fact that when 1688 is multiplied by 8, 13504 is obtained which is less than 14400. The acquired answer currently is 896 and also we bring down 00.Step 7: The quotient is now 848 and also it is multiply by 2. This gives 1696, which climate would come to be the beginning digit the the new divisor.Step 8: 5 is written at one"s place of brand-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 much we have obtained 72 = 8.485. Top top repeating this procedure further, us 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 actual number? 

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


Radius is found using the formula that area that a one is πr2 square inches. Through 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 root of 72 is 8.48 inches.

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

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

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