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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Updated on: 10-Oct-2022

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