Square Root of 81

Square Root of 81 is 9. Square Root is a number when multiplied by itself, its square root yields the original value. Assuming a to be the square root of b, the equation can be written as a = √b or as a² = b. In this case, the radical symbol “√” stands for the square root. The square of the positive number is represented by multiplying it by itself.

In this article we will discuss about square root of 81 and how to find the square root of 81.

Square Root of 81 is a number that results in 81 when multiplied by itself. Square Root of 81 is approximately equal to 9. Square root of 81 is represented as follows:

• Radical Form: √81 = 9.
• Fractional Exponent Form: (81)^1/2 = 9.

Try out the following calculator to find the square root of 81

Some of the methods are given below to find out the square root of 80.

• Square Root of 81 by Long Division Method
• Square Root 81 by Prime Factorization Method
• Square Root of 81 by Repeated Subtraction

Square Root of 81 by Long Division Method

Follow the instructions given below to find the Square Root by Long Division Method:

We need to find the square root of 81

• Step 1: As here we start with the number 81 and use decimal points with the pairing of zeroes.

• Step 2: Choose a perfect square less than or equal to 81. Since 81 is itself a perfect square. Hence divisor will be 9.

• Step 3: Since the divisor is 9, the quotient is 9 therefore dividend will be 81.

• Step 4: Subtract 81 from 81 the difference will be zero.

Therefore, the value of the square root of 81 approximately will be 9

Square Root 81 by Prime Factorization Method

Prime factorization method is a convenient or frequent way to find the square root of a number. So, let’s see the prime factorization method to simplify the square root of 81:

• Step 1: The prime factorization of 81 is 3 × 3 × 3 × 3
• Step 2: Now Let us take these factors as pairs; 81 = (3 × 3) × (3 × 3)
• Step 3: At this point, find the square root of 81.
  √81 = √{(3 × 3) × (3 × 3)}
  √81 = 3 × 3
  √81 = 9
• Step 4: Therefore, the square root of 81 is equal to 9

Square Root of 81 by Repeated Subtraction Method

To find the square root of 81 using repeated subtraction method we need to subtract 81 successively by consecutive odd numbers. The number of steps in which the difference becomes zero is the square root of 81. Let’s see the process

• 81 – 1 = 80
• 80 – 3 = 77
• 77 – 5 = 72
• 72 – 7 = 65
• 65 – 9 = 56
• 56 – 11 = 45
• 45 – 13 = 32
• 32 – 15 = 17
• 17 – 17 = 0

Here, the difference is zero in the 9th step. Hence, the square root of 81 is 9

Square root of 81 is rational. Since, square root of 81 is 9 which can be represented as a straightforward fraction in the form of p/q. Hence, square root of 81 is a rational number.

Also, Check

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What is the Square Root Value of 81?

The value of the square root of 81 is equal to 9

How do you Find the value of Root 81?

We can find the square root of 81 is find in two ways, like; Long division method, Prime Factorization Method and repeated subtraction method

Is 80 a Perfect Square?

Yes, square root of 81 is a perfect square because its square root is an integer

Square root of 81 is Rational or Irrational?

The square root of 80 is an irrational number as we know that √81 = 9.., which is an irrational number.