Simplify the following expressions:$(3+\sqrt3)(5-\sqrt2)$

Given:

$(3+\sqrt3)(5-\sqrt2)$

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,

$(3+\sqrt{3})(5-\sqrt{2})=3 \times 5-3 \sqrt{2}+5 \sqrt{3}-\sqrt{3} \times \sqrt{2}$

$=15-3 \sqrt{2}+5 \sqrt{3}-\sqrt{6}$

Hence, $(3+\sqrt{3})(5-\sqrt{2})=15-3 \sqrt{2}+5 \sqrt{3}-\sqrt{6}$.

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Updated on: 10-Oct-2022

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