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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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