Question

Which number below is irrational?a)√4/9 b) √20 c)√121Why is the number you chose irrational?

Answer 1

The number b) √20 is irrational because it cannot be expressed as a fraction. It is the square root of a non-perfect square, resulting in a non-terminating, non-repeating decimal.

Step-by-step explanation:

The number √20 is irrational. An irrational number is a number that cannot be expressed as a simple fraction, meaning it's a non-terminating and non-repeating decimal. Let's examine the given options:

• a) √4/9 equals to√2/3 which is rational because it is a fraction of two integers.
• b) √20 is irrational because 20 is not a perfect square, and the square root of a non-perfect square is an endless, non-repeating decimal.
• c) √121 equals to 11 which is rational because it represents a number that can be expressed as a simple fraction.

Therefore, √20 is the only number among the given options that is an irrational number.

Answer 2

`\begin{gathered} \sqrt[]{(4)/(9)}=\frac{\sqrt[]{4}}{\sqrt[\square]{9}}=(2)/(3)\text{ with is a fraction (its rational)} \\ \sqrt[]{20}=\sqrt[]{4\cdot5}=\sqrt[]{4}\sqrt[]{5}=2\sqrt[]{5}\text{ which is irrational} \\ \sqrt[]{121}=\sqrt[]{11^2}=11\text{ which is an integer} \end{gathered}`