What is the square root of 72

72 is not an ideal square. It is represented as √72. The square root of 72 can only be simplified. In this mini lesson we will be taught how to find the square root of 72 using long division technique along with solved examples. Let us see what the square root of 72 is.

  • Square root of 72: 72 = 8.4852
  • Square 72: 722 = 5184

1. What is the square root of 72? 2. Is the square root of 72 Reasonable or Unreasonable? 3. Learn how to Discover the Square Root of 72? 4. Frequently Asked Questions about Square Root of 72 The only quantity whose square is 72 is the square root of 72. Can you discover what that quantity is? It can be seen that there aren’t any integers where squared gives 72. Read: Square root of 72√72 = 8.4852 To check this answer we can discover (8.4852) 2 and we can see that we get a count of 71.99861904. This quantity is very close to 72 when it is rounded to its nearest value. Read more: 75 days from today Any quantity that has just ended or has not ended and has a repeating pattern in its half-decimals is a rational quantity. We find that √72 = 8.48528137423857. This number of decimals is non-terminating, and half-decimals have no repeating pattern. So it is NOT a rational quantity. Therefore, √72 is irrational.Important Notes:

  • 72 is between 64 and 81. Thus, √72 is between √64 and √81, i.e. √72 is between 8 and 9.
  • The square root of an imperfect squared quantity of the simplest kind can be discovered using prime factorization techniques. For example: 72 = 2 × 2 × 2 × 3 × 3. So, √72 = √ (2 × 2 × 2 × 3 × 3) = 6√2.
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There are completely different strategies for finding the square root of any quantity. We can discover the square root of 72 using the long division technique. Click here to know more about it.

Simplify the radical type of the square root of 72

72 is a composite quantity. Therefore, the components of 72 are 1, 2, 3, 4, 6, 8, 9 12, 18, 24, 36, and 72. When we discover the square root of any quantity, we take a quantity from each pair of similar numbers from its prime factor and we multiply them. The factor of 72 is 2 × 2 × 2 × 3 × 3 with 1 pair of the same quantity. Therefore, the simplest type of root of √72 is 6√2.

Square root of 72 using length division technique

Read more: Rhysia | Q&A about the square root of 72 can be discovered using verbose division as follows.

  • Step 1: In this step, we concatenate the digits of a certain quantity starting with a digit in the place of a person. We put a crossbar for point pairing.
  • Step 2: Now we have to find a quantity which, when squared, gives a value less than or equal to 72. As we know, 8 × 8 = 64 < 72. The resulting divisor is 8 and the quotient is 8.
  • Step 3: Now, we have to move down to 00 and multiply the quotient by 2 which gives us 16.
  • Step 4: 4 is written in place of the new divisor because when 164 is multiplied by 4, 656 is obtained less than 800. The answer obtained is now 144 and we distribute down to 00.
  • Step 5: The quotient is now 84 and it is multiplied by 2. This gives 168, which will then be changed to the first digit of the new divisor.
  • Step 6: 7 is written in the place of the new divisor because when multiplying 1688 by 8, the result is 13504 which is less than 14400. The answer obtained is now 896 and we distribute down to 00.
  • Step 7: The quotient is now 848 and it is multiplied by 2. This gives 1696, which will then change to the first digit of the new divisor.
  • Step 8: 5 is written in place of the new divisor because when 16965 is multiplied by 8, the yield 84825 is lower than 89600. The answer obtained is now 4775 and we distribute down to 00.
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Up to this point, we have obtained √72 = 8.485. When repeating this addition process, we get, √72 = 8.48528137423857Explore square roots using interactive illustrations and examples.

  • Square root of 61
  • Square root of 63
  • Square root of 65
  • Square root of 68
  • Square root of 85

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  • Are √-72 and –√72 the same?
  • Is √-72 a practical quantity?

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