MathsQuestion

what is the square root of 81?

The square root of 81 is 9.

Certainly, let’s break down the calculation of the square root of 81 in detail:

The square root of a number is a value that, when multiplied by itself, gives the original number. In mathematical notation, the square root of a number “x” is represented as √x.

For the number 81, we want to find its square root (√81). To do this, we can use various methods, such as long division or estimation, but one common method is using prime factorization.

Step 1: Prime Factorization of 81

Prime factorization involves breaking down the number into its prime factors. The prime factorization of 81 is:

81 = 3^4

This means that 81 can be expressed as 3 raised to the power of 4.

Step 2: Finding the Square Root

To find the square root of 81, we can use the prime factorization. Since 81 is 3 raised to the power of 4, we can take half of the exponent (4) to find the square root:

√81 = √(3^4) = 3^(4/2) = 3^2 = 9

So, the square root of 81 is indeed 9.

In summary, the square root of 81 is calculated by recognizing that 81 can be expressed as 3 raised to the power of 4. Taking half of the exponent gives us 3 raised to the power of 2, which is 9. Therefore, √81 = 9.

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