Question

Find two rational number and two irrational numbers between 3 root 8 and root 9

Answer 1

Step-by-step explanation:

here is the answer of this question and please mark brilliant

Answer 2

Two rational numbers between 2 and 3 are 2.5 and 2.75, and two irrational numbers between 2 and 3 are √6 and √(15/2).

Given:

Two numbers ∛8 and √9.

To Find:

Two rational and two irrational numbers between ∛8 and √9.

Solution:

We know that ∛8 = 2 and √9 = 3.

So our question is to find two rational and two irrational numbers between 2 and 3.

If 'a' and 'b' are two rational numbers, then $\frac{a+b}{2}$ is also a rational number.

Since 2 and 3 are rational numbers, $\frac{2+3}{2}$ = 2.5 is a rational number between 2 and 3.

Now, 2.5 and 3 are rational numbers, so $\frac{2.5+3}{2}$ = 2.75 is also a rational number between 2 and 3.

Hence, 2.5 and 2.75 are two rational numbers between 2 and 3.

If 'a' and 'b' are two rational numbers, then ​$\sqrt{ab}$, given that ab is not a perfect square, is an irrational number.

Since 2 and 3 are rational numbers and 2x3=6 is not a perfect square, √(2x3) =√6 is an irrational number between 2 and 3.

We also know that 2.5 and 3 are two rational numbers between 2 and 3, and 2.5x3 = 7.5 = 75/10 = 15/2 is not a perfect square.

So √(2.5x3) = √(15/2) is an irrational number.

Hence, √6 and √(15/2) are two irrational numbers between 2 and 3.

∴ Two rational numbers between 2 and 3 are 2.5 and 2.75, and two irrational numbers between 2 and 3 are √6 and √(15/2).

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