Write 2 different irrational number lying between $\frac{3}{7}$&$ \frac{1}{11}$.

To do: Write two irrational number between $\frac{3}{7}$&$ \frac{1}{11}$

Solution:

To solve this question, first we need to find LCM of the denominators and convert them into like fractions.

LCM of denominators 7 and 11 is 77.

To convert into like fractions

• We will multiply numerator and denominator of $\frac{3}{7}$ with 11. 
  $\frac{3}{ 7} = \frac{3}{7}\times\frac{11}{11} = \frac{33}{77}$
  
• we will multiply numerator and denominator of $\frac{1}{11}$ with 7.
  $\frac{1}{11}= \frac{1}{11}\times\frac{7}{7} = \frac{7}{77}$
  

Now our numbers are $\frac{7}{77} $ and $ \frac{33}{77}$.

Now in between the numerators 7 and 33, we have to find irrational numbers.

We know $7 =\sqrt{49}$So, $\sqrt{50}$and$\sqrt{51}$ are greater than 7.

So the two irrational numbers are $\frac{\sqrt{50}}{77} \ and \ \frac{\sqrt{51}}{77}$

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Updated on: 10-Oct-2022

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