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

Answer :

Answer:

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

Step-by-step 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.

[tex]d^2 = l^2 + l^2[/tex]

[tex]d^2 = 2l^2[/tex]

Take positive square root of both sides

[tex]d = \sqrt{2l^2}[/tex]

Split:

[tex]d = \sqrt{2} * \sqrt{l^2}[/tex]

[tex]d = \sqrt{2} *l[/tex]

Recall that the side length (l) is rational.

However, [tex]\sqrt 2[/tex] is irrational.

So, the product of l and [tex]\sqrt 2[/tex] will be irrational

Hence:

The diagonal is irrational

Go Question: Other Questions