An irrational number between 2 and 3 is: 1. (2+3 ) 2. (2 3 ) 3. 5^ 1 4 4. 6^ 1 4

4. 6^ 1 4 Solution: An irrational number between a and b is given by ab An irrational number between 2 and 3 is 2+3 = (6 )^ 1 2 =6^ 1 2 1 2 =6^ 1 4 Hence, the correct answer is option (d).

An irrational number between 2 and 3 is: 1. (2+3 ) 2. (2 3 ) 3. 5…

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Question

An irrational number between $\sqrt{2}$ and $\sqrt{3}$ is:

$\big(\sqrt{2}+\sqrt{3}\big)$
$\big(\sqrt{2}\times\sqrt{3}\big)$
$5^{\frac{1}{4}}$
$6^{\frac{1}{4}}$

✓

Answer

$6^{\frac{1}{4}}$

Solution:
An irrational number between a and b is given by $\sqrt{\text{ab}}$
An irrational number between $\sqrt{2}$ and $\sqrt{3}$ is
$\sqrt{\sqrt{2}+\sqrt{3}}=\big(\sqrt{6}\big)^{\frac{1}{2}}$
$=6^{\frac{1}{2}\times\frac{1}{2}}$
$=6^{\frac{1}{4}}$
Hence, the correct answer is option (d).

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