Now consider the product of a nonzero rational number and an irrational number. Again, assume x = , where a and b are integers and b ≠ 0. This time let y be an irrational number. If we assume the product x · y is rational, we can set the product equal to , where m and n are integers and n ≠ 0. The steps for solving this equation for y are shown. Based on what we established about the classification of y and using the closure of integers, what does the equation tell you about the type of number y must be for the product to be rational? What conclusion can you now make about the result of multiplying a rational and an irrational number?

Irrational number

Step-by-step explanation:

It's given,

y = (By simplifying the product of rational number 'x' and an irrational number 'y')

Where m and n are the integers and is a rational number.

(Since x = is a rational number)

Therefore, will be a rational number.

y = ⇒ Irrational number = Rational number

which is a contradictory statement.

Therefore, multiplication of rational and irrational number will be irrational.

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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