Question

find value of p step by step
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Answer 1

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$\sqrt{13 + p \sqrt{10} } = \sqrt{8} + \sqrt{5} \\ 13 + p \sqrt{10} = ( \sqrt{8} + \sqrt{5} ) {}^{2} \\ 13 + p \sqrt{10} = 8 + 5 + 2 \sqrt{40} \\ 13 + p \sqrt{10} = 13 + 2 \sqrt{40} \\ p \sqrt{10} = 2 \sqrt{40} \\ p = \frac{2 \sqrt{40} }{ \sqrt{10} }$