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Estimate the value of the irrational number (0.6289731...)2. Up to how many decimal digits is the estimation correct? 4 5 6 7

User Stig Perez
by
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2 Answers

3 votes

Answer:

6

Explanation:

I dont know?

User Jose Rocha
by
7.3k points
1 vote

Answer:

0.927

Explanation:

The value can be estimated using the binomial theorem for expanding numbers. The theorem states:

For an expansion


(1+x)^(n) = 1+ (n)/(1)x+(n(n-1))/(1*2) x^(2) + ...

Now, let's take the value 0.6289731. In the expression, let 0.6289731 be equal to
( 1 - 0.0371)

We can use the binomial expansion above:


(1-0.0371)^(2) = 1+ (-)((2))/(1) (0.0371) + (2(2-1))/(1*2) (-0.0371)^(2) + ... up to three terms

This gives 1-0.0734+0.00137641 = 0.927 up to 3 decimal places

User Eric Lafortune
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7.8k points

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