Question

State True or False.
Insert three rational numbers between 5 and 7.

Answer 1

Hint: Here, we need to prove that if the given answer satisfies the given statement in the question. Hence, we will check if the answers provided lie between the given numbers 5 and 7 or not. If yes, then we will mark the statement true, otherwise, false.

Complete step by step Answer:

Let us assume that we need to find the solution irrespective of the fact that we are given an answer.
We have to insert 3 rational numbers between 5 and 7.
Therefore, rational numbers must lie between 5 and 7.
Given rational numbers which are said to be inserted between 5 and 7 are $\sqrt {26} ,\sqrt {27} and\sqrt {29} $ .
Now, we have ${5^2} = 25,{7^2} = 49$
Therefore, if we have any 3 numbers which need to be inserted between 5 and 7, then their squares must lie between the squares of 5 and 7.
$ \Rightarrow 25$< $26,27,29$ < $49$
Hence, we can say that the squares of the given numbers lie between the squares of 5 and 7.
Therefore, the given answers are correct as they lie between 5 and 7.

So, we can say that the given statement is true.

Note: In such problems, we only need to check if the given answers are justified or not. The statement will simultaneously be proven true or false. Here, we were given answers already so we did not need to solve the question for three rational numbers that can be inserted between 5 and 7. We just checked if the answers provided were true or not.