1) Which of the following is a surd ? a) 64 b) 6 root 64 c) 4 root 64 d) 3 root 64

Mathematics

1 answer:

Mashcka [7]2 years ago

5 0

Answer:

$\text{c) }\sqrt[4]{64}=2\sqrt[4]{4}$

Step-by-step explanation:

$\text{a) }64\qquad\text{an integer; not a surd}\\\\\text{b) }\sqrt[6]{64}=2\qquad\text{an integer; not a surd}\\\\\text{c) }\sqrt[4]{64}=2\sqrt[4]{4}\qquad\textbf{a surd}\\\\\text{d) }\sqrt[3]{64}=4\qquad\text{an integer; not a surd}$

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If $k$ is odd, then

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In the odd case, instead of considering the above equation we can consider the partial sums. If $k$ is odd, then the sum of the even integers between 1 and $k$ would be

$S=2+4+6+\cdots+(k-5)+(k-3)+(k-1)$

Now consider the partial sum up to the second-to-last term,

$S^*=2+4+6+\cdots+(k-5)+(k-3)$

Subtracting this from the previous partial sum, we have

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