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(⁴√2+⁴√8)²

Sagot :

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Answer:

Simplified = 4 + 3[tex]\sqrt{2}\\[/tex], Decimal = 8.2426...

Step-by-step explanation:

Loneguyidn

[tex]\left( \sqrt[4]{2} + \sqrt[4]{8} \right)^2\\\\=\left(\sqrt[4]2\right)^2 + \left(\sqrt[4]8\right)^2 + 2 \sqrt[4]2 \cdot \sqrt[4]8\\\\\\= \left(2^{\tfrac 14} \right)^2 + \left(8^{\tfrac 14} \right)^2+2\sqrt[4]{16}\\\\\\= 2^{\tfrac 12} +8^{\tfrac 12} + 2 \cdot \left(16\right)^{\tfrac 14}\\\\=\sqrt 2 +\sqrt 8+2 \cdot \left(2^4\right)^{\tfrac 14}\\\\=\sqrt 2 + \sqrt{4\times 2}+2\cdot 2\\\\= \sqrt 2 + 2\sqrt 2+4\\\\=4+ 3\sqrt 2[/tex]

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