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In this paper, we mainly discuss the monotonicity of some sequences related to the hyperfibonacci sequences \( \{F_{n}^{[r]}\}_{n\geq 0} \) and the hyperlucas sequences \( \{L_{n}^{[r]}\}_{n\geq 0} \), where \( r \) is a positive integer. We prove that \( \{\sqrt[n]{F_{n}^{[1]}}\}_{n\geq 1} \) and \( \{\sqrt[n]{F_{n}^{[2]}}\}_{n\geq 1} \) are unimodal and \( \{\sqrt[n]{L_{n}^{[1]}}\}_{n\geq 1} \), \( \{\sqrt[n]{F_{n+1}^{[1]}/{F_{n}^{[1]}}}\}_{n\geq 1} \), and \( \{\sqrt[n]{L_{n+1}^{[1]}/{L_{n}^{[1]}}}\}_{n\geq 2} \) are decreasing. Furthermore, we discuss the monotonicity of the sequences
\[
\left\{\frac{\sqrt[n+1]{F_{n+1}^{[1]}}}{\sqrt[n]{F_{n}^{[1]}}}\right\}_{n\geq 1} \text{ and } \left\{\frac{\sqrt[n+1]{L_{n+1}^{[1]}}}{\sqrt[n]{L_{n}^{[1]}}}\right\}_{n\geq 1}
\]