How do you find the square root of 81?

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ol3i4c5s4hr · Accepted Answer

The square root is 81  ±9⋅9  ±9

Pademagk71 · Accepted Answer

Explanation:  81=9⋅9 then the square root of 81=9  Because the double multiplication for the same sign is always positive, the square root is also valid with the other sign 81=(−9)⋅(−9) then 81=−9 and we can say that 81=±9  What if we do not know the value? There is an algorithm to calculate the square root quite simple (the Babylonian algorithm).  We want to calculate the square root of 81, we first guess a possible value. For example we know that 10⋅10=100 and 7⋅7=49, then we can imagine that the square root of 81 is between 7 and 10, we can imagine for example 8.3.  Then the algorithm tell us that the next step of approximation is given by  xn+1=12xn+αxn where alpha is the number that we are searching the square root (for us α=81) and xn is our guess. Our first guess is x1=8.3, then the next step of approximation is  x2=128.3+818.3=9.029518  I continue with the next approximation  x3=129.029518+819.029518=9.0000482  x4=129.0000482+819.0000482=9.0000000013  x5=129.0000000013+819.00000000000013=9 (my computer does not approximate more).  As you can see in few steps the algorithm converges to the square root. Of course, because the previous discussion about the positive and negative sign, also the same result with the minus sign is a solution of the square root.

karton · Accepted Answer

The square root of a number is that number which, when multiplied by itself will give the original number: y=?×?=? 25=5×5=5 x2=x×x=x x6y8=x3y4 To find any root of a number, write the radicand as the product of its prime factors: 81=(3×3)×(3×3)=3×3=9 You can now understand this in different ways: 81=(3×3)×(3×3)=3×3=9 81=(3×3)×(3×3)=9×9=9 81=34=34÷2=32=9

How do you find the square root of 81?

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