Question

find the squar root of the given in the form of a binomial surd : 14+6√5​

Answer 1

Answer:

$\sqrt{14+6\sqrt{5}}=3+\sqrt{5}$

Step-by-step explanation:

$\sqrt{14+6\sqrt{5}}\\=\sqrt{14+2\sqrt{9\times 5}}\\= \sqrt{9+5+2\sqrt{9\times 5}}\\=\sqrt{(\sqrt{9})^{2}+(\sqrt{5})^{2}+2\times \sqrt{9}\times \sqrt{5}}\\=\sqrt{(\sqrt{9}+\sqrt{5})^{2}}\\=\sqrt{9}+\sqrt{5}\\=3+\sqrt{5}$

Therefore,

$\sqrt{14+6\sqrt{5}}=3+\sqrt{5}$

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Answer 2

Answer:

Step-by-step explanation: