The Beginings of Greek Mathematics

Which one of the following is irrational number ?

• √2

• 5

• 7/8

• 0.97

Between X and Y, which is the (Side) and which is the (Diagonal)?

• X = Side and Y = Diagonal

• X = Diagonal and Y = Side

Based on diagram shown, what are the values of X₈ and Y₈

• X₈= 408 , Y₈=577

• X₈= 408 , Y₈=239

• X₈= 169 , Y₈=577

Using side and diagonal number we can consider the ratios y_n/x_n , then we find that as n increases the quotient is

1, 3/2, m, 17/12, …what is value of m ?

• 1.4

• 2

• 4.25

when n →∞, it is approaching to √2

• True

• False

There are 3 steps to find an approximation of √2. The steps are, find Xn and Yn, determine the sign and ____.

• Completing the square

• Line Number

• Compute the square root

• Modified Formula

We can use side and diagonal number to find approximation of √2

• True

• False

I. using modified formula

II. using original formula

III. by completing the square

IV. by factorization

• I and III

• II and IV

• I and II

• All the above

Using the formula given, choose the best answer that is nearer the approximation

• nearer approximation of  $\sqrt{1}$  

• nearer approximation of  $\sqrt{2}$  

• nearer approximation of  $\sqrt{1.5}$  

• nearer approximation of  $\sqrt{3}$  

These are THREE construction problems of antiquity except.

• The squaring of circle

• The duplication of cube

• The pythagoras theorem

• The trisection of angle