72 is no a perfect square. It is stood for as 72. The square source of 72 can only be simplified. In this mini-lesson we will find out to find square source of 72 by long department method in addition to solved examples. Let us see what the square source of 72 is.

You are watching: Find the square root of 144

Square source of 7272 = 8.4852Square that 72: 722 = 5184
 1 What Is the Square root of 72? 2 Is Square root of 72 rational or Irrational? 3 How to uncover the Square source of 72? 4 FAQs on Square source 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 watched that there room no integers who square provides 72.

72 = 8.4852

To inspect this answer, we can discover (8.4852)2 and we can see that we gain a number 71.99861904. This number is really close come 72 when that is rounded come its nearest value.

Any number i beg your pardon is either terminating or non-terminating and also has a repeating pattern in that is decimal part is a rational number. We experienced that 72 = 8.48528137423857. This decimal number is non-terminating and the decimal part has no repeating pattern. So the is no a reasonable number. Hence, 72 is one irrational number.

Important Notes:

72 lies in between 64 and 81. Hence, 72 lies in 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. Because that example: 72 = 2 × 2 × 2 × 3 × 3. So, 72 = (2 × 2 × 2 × 3 × 3) = 62.

## How to uncover the Square source of 72?

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

### Simplified Radical type of Square source of 72

72 is a composite number. Hence factors that 72 are 1, 2, 3, 4, 6, 8, 9 12, 18, 24, 36, and 72. When we uncover the square source of any type of number, we take one number from every pair the the exact same numbers from its element factorization and we main point them. The factorization of 72 is 2 × 2 × 2 × 3 × 3 which has 1 pair of the exact same number. Thus, the most basic radical kind of √72 is 62.

### Square root 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, us pair turn off digits the a provided number starting with a digit at one"s place. We placed a horizontal bar come indicate pairing.Step 2: Now we require to discover a number i beg your pardon on squaring offers value less than or same to 72. Together we know, 8 × 8 = 64 Step 3: Now, we have actually to carry down 00 and also multiply the quotient by 2 which provides us 16. Step 4: 4 is written at one"s location of new divisor since 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 now 84 and it is multiplied by 2. This gives 168, which climate would come to be the beginning digit that the new divisor.Step 6: 7 is written at one"s location of new divisor because when 1688 is multiplied by 8, 13504 is obtained which is much less than 14400. The acquired answer currently 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 become the starting digit the the new divisor.Step 8: 5 is written at one"s location of new divisor because when 16965 is multiplied by 8, 84825 is acquired which is less than 89600. The acquired answer now is 4775 and we lug down 00.

So far we have obtained 72 = 8.485. On repeating this process further, we get, 72 = 8.48528137423857

Explore square roots utilizing illustrations and interactive examples.

Think Tank:

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

Example 2: Is the radius the 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 the area that a one is πr2 square inches. By the offered 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.

See more: What Is A Relatively Prime Number, The Prime Glossary: Relatively Prime

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

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

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