Simplify the following expressions:$(\sqrt5-2)(\sqrt3-\sqrt5)$

Given:

$(\sqrt5-2)(\sqrt3-\sqrt5)$

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,

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

$=\sqrt{15}-(\sqrt{5})^2-2 \sqrt{3}+2 \sqrt{5}$

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

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

Hence, $(\sqrt5-2)(\sqrt3-\sqrt5)=\sqrt{15}-2 \sqrt{3}+2 \sqrt{5}-5$.

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Updated on: 10-Oct-2022

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