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rosijanka [135]
3 years ago
14

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">
Mathematics
2 answers:
masya89 [10]3 years ago
6 0

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!

<h3>~AH1807</h3>
dsp733 years ago
5 0
<h3>Solution:</h3>

( \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}

<h3>Answer:</h3>

7 + 6√2

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