Question

Identify the number that does not belong with the other three. Explain your reasoning. 50.1 repeating 1, negative 50 over 2, negative 50.1, square root 50

Answer 1

square root 50 does not belong....all of the other numbers are rational numbers. square root 50 is irrational.

Answer 2

Given:

The four values are $50.111..., -\dfrac{50}{2},-50.1,\sqrt{50}$.

To find:

The number that does not belong with the other three.

Solution:

Rational number: If a number can be defined in the form of $\dfrac{p}{q}$, where $p,q$ are integers and $q\neq 0$, then it is called a rational number.

For example: $3, -0.5,\dfrac{1}{5}$ etc.  

Irrational number: If a number cannot be defined in the form of $\dfrac{p}{q}$, where $p,q$ are integers and $q\neq 0$, then it is called an irrational number.  

For example: $\sqrt{7}, -\sqrt{2}$ etc.

We know that the numbers with recurring (repeating) decimals are rational numbers. So, 50.1 repeating 1 is a rational number.

Clearly, $-\dfrac{50}{2},-50.1$ are also rational numbers.

$\sqrt{50}=\dfrac{2\times 25}$

$\sqrt{50}=5\dfrac{2}$

We know that $\sqrt{2}$ is an irrational number, so $\sqrt{50}$ is also an irrational number.

The number $\sqrt{50}$ does not belong with the other three because it is irrational number and other three are rational numbers.

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