Question

1" title="\left(\sqrt{2}+1\right)\left(5+\sqrt{2}\right)" alt="\left(\sqrt{2}+1\right)\left(5+\sqrt{2}\right)" align="absmiddle" class="latex-formula">

Answer 1

Answer:

$\huge\boxed{\sf 7 + 6\sqrt{2}}$

Step-by-step explanation:

$(\sqrt{2} +1)(5+\sqrt{2} )\\\\= \sqrt{2} (5+\sqrt{2} )+1(5+\sqrt{2} )\\\\= 5\sqrt{2} + (\sqrt{2})^2+5+\sqrt{2} \\\\= 5\sqrt{2} + 2 + 5 + \sqrt{2} \\\\= 2+5+\sqrt{2} + 5\sqrt{2} \\\\= 7 + \sqrt{2} (1+5)\\\\= 7 + 6\sqrt{2} \\\\\rule[225]{225}{2}$

Hope this helped!

~AH1807

Answer 2

Solution:

$( \sqrt{2} + 1)(5 + \sqrt{2}) \\ = \sqrt{2} (5 + \sqrt{2} ) + 1(5 + \sqrt{2} ) \\ = 5 \sqrt{2} + 2 + 5 + \sqrt{2} \\ = 7 + 6 \sqrt{2}$

Answer:

7 + 6√2