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Simplify the following expressions:
$(4+\sqrt7)(3+\sqrt2)$
Given:
$(4+\sqrt7)(3+\sqrt2)$
To do:
We have to simplify the given expression.
Solution:
We know that,
$(a^{m})^{n}=a^{m n}$
$a^{m} \times a^{n}=a^{m+n}$
$a^{m} \div a^{n}=a^{m-n}$
$\sqrt[n]{a} \times \sqrt[n]{b}=\sqrt[n]{a \times b}$
$\sqrt[n]{a} \div \sqrt[n]{b}=\sqrt[n]{\frac{a}{b}}$
$a^{0}=1$
Therefore,
$(4+\sqrt{7})(3+\sqrt{2})=4 \times 3+4 \times \sqrt{2}+3 \times \sqrt{7}+\sqrt{7} \times \sqrt{2}$
$=12+4 \sqrt{2}+3 \sqrt{7}+\sqrt{14}$
Hence, $(4+\sqrt7)(3+\sqrt2)=12+4 \sqrt{2}+3 \sqrt{7}+\sqrt{14}$.
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