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Crazy boy [7]
2 years ago
5

What is the simplified form of the following expression? Assume x greater-than-or-equal-to 0 and y greater-than-or-equal-to 0

Mathematics
1 answer:
Bogdan [553]2 years ago
5 0

Answer:

  \text{(c) }\ 13\sqrt[4]{x}-10\sqrt[4]{2y}

Step-by-step explanation:

Simplification of radical expressions of this sort involves ...

  • factoring out integer powers
  • combining like terms

The given expression can be simplified as follows:

  \displaystyle 2\sqrt[4]{16x}-2\sqrt[4]{2y}+3\sqrt[4]{81x}-4\sqrt[4]{32y}\\\\=2\sqrt[4]{2^4x}-2\sqrt[4]{2y}+3\sqrt[4]{3^4x}-4\sqrt[4]{2^4(2y)}\\\\=2\cdot2\sqrt[4]{x}-2\sqrt[4]{2y}+3\cdot3\sqrt[4]{x}-4\cdot2\sqrt[4]{2y}\\\\=(2\cdot2+3\cdot3)\sqrt[4]{x}-(2+4\cdot2)\sqrt[4]{2y}\\\\=\boxed{13\sqrt[4]{x}-10\sqrt[4]{2y}}

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