72 is no a perfect square. It is stood for as 72. The square source of 72 have the right to only be simplified. In this mini-lesson us will learn to uncover square source of 72 by long department method along with solved examples. Let us see what the square source of 72 is.

You are watching: Simplify the square root of 24

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

The original number whose square is 72 is the square root of 72. Deserve to you discover what is the number? It can be checked out that there are no integers whose square gives 72.

72 = 8.4852

To examine this answer, we can uncover (8.4852)2 and we deserve to see that we gain a number 71.99861904. This number is an extremely close come 72 when that rounded to its nearest value.

Any number which is either terminating or non-terminating and has a repeating pattern in that decimal part is a rational number. We witnessed that 72 = 8.48528137423857. This decimal number is non-terminating and the decimal component has no repeating pattern. So that is no a rational 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 source of a non-perfect square number in the simplest radical kind 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 source of 72?

There room different methods to find the square root of any kind of number. We can find the square source of 72 utilizing long division method.Click here to know an ext about it.

Simplified Radical kind of Square root of 72

72 is a composite number. Hence factors the 72 are 1, 2, 3, 4, 6, 8, 9 12, 18, 24, 36, and also 72. Once we discover the square root of any kind of number, us take one number from every pair that the 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 exact same number. Thus, the easiest radical kind of √72 is 62.

Square source of 72 by Long department Method

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

Step 1: In this step, we pair turn off digits of a provided number beginning with a digit at one"s place. We put a horizontal bar come indicate pairing.Step 2: Now we need to uncover a number i m sorry on squaring gives 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 through 2 which offers us 16. Step 4: 4 is written at one"s location of new divisor because when 164 is multiply by 4, 656 is obtained which is much less than 800. The acquired answer currently is 144 and we carry down 00.Step 5: The quotient is currently 84 and it is multiply by 2. This gives 168, which then would become the beginning digit of the new divisor.Step 6: 7 is written at one"s ar of new divisor since when 1688 is multiply by 8, 13504 is acquired which is less than 14400. The acquired answer now is 896 and also we lug down 00.Step 7: The quotient is currently 848 and also it is multiply by 2. This gives 1696, which then would end up being the starting digit of the new divisor.Step 8: 5 is written at one"s ar of new divisor since when 16965 is multiplied by 8, 84825 is acquired which is much less than 89600. The obtained answer currently is 4775 and we bring down 00.


So far we have acquired 72 = 8.485. ~ above repeating this procedure 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 of a circle having area 72π square inches same 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 acquisition the square source on both sides, √r2= 72. We know that the square source of r2 is r.The square source of 72 is 8.48 inches.

See more: How Many Grams In 8 Ounces? 8 Ounces To Grams Conversion Calculator

The length of square is found using the formula that area that square. Together per the given information,

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

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