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The length, in millimeters of each side of a square shaped electronic chip is a rational number. What statement is true about the length of the diagonal of the chip

User RHarris
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1 Answer

7 votes

Answer:

The diagonal is irrational because it is a product of a rational and an irrational number

Explanation:

The options are not given. However, the question is still answerable.

Given

Shape: Square

Length: Rational

Since the side length is said to be rational, I'll answer the question based on whether the diagonal is rational or not.

Having said that:

The diagonal (d) of a square with side length (l) is calculated using Pythagoras theorem.


d^2 = l^2 + l^2


d^2 = 2l^2

Take positive square root of both sides


d = √(2l^2)

Split:


d = √(2) * √(l^2)


d = √(2) *l

Recall that the side length (l) is rational.

However,
\sqrt 2 is irrational.

So, the product of l and
\sqrt 2 will be irrational

Hence:

The diagonal is irrational

User DrKoch
by
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