Square Root of 72

Square Root of 72 is 8.4828. The square root of 72 is an irrational expression, i.e. it is non-terminating and non-repeating in nature. Square root of a number is the number which when multiplied with itself results in the original number. Hence, the square root of 72 i.e. 8.4828... when multiplied by itself results in 72.

In this article, we will learn in detail about square root of 72, how to find it using different methods.

👁 Square-Root-of-72

What is the Square Root of 72?

The square root of 72 is denoted as √72. It is an irrational number, meaning it doesn't result in a perfect square. Its numerical value has an infinite decimal expansion. While the precise decimal representation of √72 goes on indefinitely, for practical use, it is often rounded to a specific number of decimal places.

Square Root of 72 is given as:

√72 = 8.48528137423857...

The above decimal expansion is approximated to 8.485 (rounded to three decimal places)

Square Root of 72 Calculator

Try out the following calculator to find out the square root of 72

How to Find the Square Root of 72?

As mentioned, the square root of a number is a whole number that when multiplied with itself, gives the original number.

We can find the square root of 72 using the following two methods:

• Square Root 72 Value by Long Division Method
• Square Root of 72 Using Prime Factorization

Let’s learn, these methods in detail.

Square Root 72 using Long Division Method

Follow the following mentioned steps to find the square root of 6 using the long division method

Step 1: Start with the number 72.000000 and start pairing its from right to left

Step 2: Choose a perfect square less than 72 as the initial dividend (e.g., 64). Hence divisor will be 8.

Step 3: Since, divisor is 8, quotient is 8 therefore dividend will be 64. Subtract 64 from 72 and add 8 in the divisor

Step 4: New divisor is 16, dividend is 8. Now put decimal after 8 in quotient and bring down two zeros. Therefore new dividend is 800

Step 5: Add a digit at left of 16 in divisor i.e. at unit place and also place the same digit in quotient such that the product is near to 800.

Step 6: Add 4 in divisor using step 5 hence, new dividend will be 164 × 4 = 656. Subtract 656 from 800

Step 7: Repeat the steps 4, 5 and 6 to find square root up to 3 or 4 decimal places as per requirement.

Learn, Square Root by Long Division

Prime Factorization Method

Step 1: Break Down 72 into Prime Factors. Hence, 72 = 2 × 2 × 2 × 3 × 3

Step 2: Group the prime factors into pairs of the same number (2 and 3 in this case).

Step 3: Find the square roots of each pair.

Step 4: Hence, √( 2 × 2 × 2 × 3 × 3) = 6√2

Is Square root 72 Rational or Irrational?

Square Root of 72 is an irrational number. In the case of √72, the decimal expansion is non terminating and non repeating. This never-ending decimal expansion is a characteristic of irrational numbers.

So, in simpler terms, the square root of 72 is irrational.

Learn More,

• Square Root
• Square Root Symbol