Simplify the following expressions:$ (11+\sqrt{11})(11-\sqrt{11}) $


Given:

\( (11+\sqrt{11})(11-\sqrt{11}) \)

To do: 

We have to simplify the given expression.

Solution:

We know that,

$(a^{m})^{n}=a^{m n}$

$a^{m} \times a^{n}=a^{m+n}$

$a^{m} \div a^{n}=a^{m-n}$

$\sqrt[n]{a} \times \sqrt[n]{b}=\sqrt[n]{a \times b}$

$\sqrt[n]{a} \div \sqrt[n]{b}=\sqrt[n]{\frac{a}{b}}$

$a^{0}=1$

$(a+b)(a-b)=a^2-b^2$

Therefore,

$(11+\sqrt{11})(11-\sqrt{11})=(11)^{2}-(\sqrt{11})^{2}$

$=121-11$

$=110$

Hence, $(11+\sqrt{11})(11-\sqrt{11})=110$. 

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Updated on: 10-Oct-2022

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