Question

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

Answer 1

6

Explanation:

I dont know?

Answer 2

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