Write the correct answer in the following: 1 9-8 is equal to 1. 1 2 (3-22) 2. 1 3+22 3. 3-22 4. 3+22

4. 3+22 Solution: 1 9-8 =1 3-22 =1 3-22 3+22 3+22 [ 8=2 2 2=22] [multiplying numerator and denominator by 3+22] 3+22 9-(2-2)^2 [using identity (a-b)(a+b)=a^2-b^2] = 3+22 9-8 =3+22

Write the correct answer in the following: 1 9-8 is equal to 1. 1…

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Question

Write the correct answer in the following:
$\frac{1}{\sqrt{9}-\sqrt{8}}$ is equal to

$\frac{1}{2}(3-2\sqrt{2})$
$\frac{1}{3+2\sqrt{2}}$
$3-2\sqrt{2}$
$3+2\sqrt{2}$

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Answer

$3+2\sqrt{2}$

Solution:
$\frac{1}{\sqrt{9}-\sqrt{8}}=\frac{1}{3-2\sqrt{2}}=\frac{1}{3-2\sqrt{2}}\cdot\frac{3+2\sqrt{2}}{3+2\sqrt{2}}$ $[\because\sqrt{8}=\sqrt{2\times2\times2}=2\sqrt{2}]$
$[$multiplying numerator and denominator by $3+2\sqrt{2}]$
$\frac{3+2\sqrt{2}}{9-(2-\sqrt{2})^2}$$[\text{using identity (a}-\text{b})(\text{a+b})=\text{a}^2-\text{b}^2]$
$=\frac{3+2\sqrt{2}}{9-8}=3+2\sqrt{2}$

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