Question

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 1

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.

$d^2 = l^2 + l^2$

$d^2 = 2l^2$

Take positive square root of both sides

$d = \sqrt{2l^2}$

Split:

$d = \sqrt{2} * \sqrt{l^2}$

$d = \sqrt{2} *l$

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