Question

Simplify each of the following expressions:
1. (3 + √3) (2 + √2)
2. (3 + √3) (3 - √3)
3. (√5 + √2)²
4. (√5 - √2) (√5 + √2)​

Correct will be marked Brainliest

Answer 1

$1. (3+\sqrt{3})(2+\sqrt{2}) \\= 3(2+\sqrt{2}) + \sqrt{3}(2+\sqrt{2})\\= 6 + 3\sqrt{2} + 2\sqrt{3} + \sqrt{6}$

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

$\boxed { \pink { Since, (a+b)(a-b) = a^{2} - b^{2} }}$

$= 9 - 3 \\ = 6$

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

$\boxed { \pink { (a+b)^{2} = a^{2} + 2ab +b^{2} }}$

$= 5 + 2\sqrt{10} + 2 \\= 7 + 2\sqrt{10}$

$4. (\sqrt{5} - \sqrt{2})( \sqrt{5} + \sqrt{2}) \\= (\sqrt{5})^{2} - (\sqrt{2})^{2}\\= 5 - 2\\= 3$

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Answer 2

here are the answers with explanation