Question

State true or false.

$\sqrt{3}+\sqrt{4}$ is an rational number.

• A. True
• B. False

Answer 1

The correct option is B False

A rational number is a number that can be written as a ratio. That means it can be written as a fraction, in which both the numerator (the number on top) and the denominator (the number on the bottom) are whole numbers.

$\Rightarrow$ All numbers that are not rational are considered irrational. An irrational number can be written as a decimal, but not as a fraction.

$\sqrt{3}=1.732$ is an irrational.

$\sqrt{4}=2$ is rational.

Now,

$\Rightarrow$ $\sqrt{3}+\sqrt{4}=1.732+2$

$=3.732$

$3.732$ cannot be converted into fraction.

$\therefore$ $\sqrt{3}+\sqrt{4}$ is an irrational number.

$\therefore$ Given statement is false.