SOLUTION: Calculate by means of the binomial theorem the value of(16.32)^1/2 to 5 decimal places

Question 1153897: Calculate by means of the binomial theorem the value of(16.32)^1/2 to 5 decimal places
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
Consider the binomial theorem:

+...+
where is a positive integer and is choose

Since the binomial theorem only works on values in the form of a binomial:
Consider that
then will be
By applying the binomial theorem, we get:

Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

Here are the first few terms of the expansion of (a+b)^n using the binomial theorem.

When n is not a positive integer, we want to write the numbers in expanded form:

etc....

Then the first few terms of the expansion are

Now we can plug in n=0.5, a=16, and b=0.32 to find the square root of 16.32 to several decimal places.

So we have the square root of 16.32, using the first four terms of the binomial expansion of , as being

The actual value to 9 decimal places is 4.039801975, so our approximation is good to 6 decimal places.

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