Question

3. Найдите сложный радикат:
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Answer 1

$\sqrt{15-\sqrt{29}}=\sqrt{\frac{15+\sqrt{15^{2}-29}}{2}}-\sqrt{\frac{15-\sqrt{15^{2}-29}}{2}}=\sqrt{\frac{15+\sqrt{225-29}}{2}} -\sqrt{\frac{15-\sqrt{225-29}}{2}}=\\\\=\sqrt{\frac{15+\sqrt{196}}{2}}-\sqrt{\frac{15-\sqrt{196}}{2}}=\sqrt{\frac{15+14}{2}}-\sqrt{\frac{15-14}{2}}=\sqrt{\frac{29}{2}}-\sqrt{\frac{1}{2}}=\\\\=\frac{\sqrt{29}}{\sqrt{2}}-\frac{1}{\sqrt{2}}= \frac{\sqrt{29}-1 }{\sqrt{2}}=\boxed{\frac{\sqrt{2}(\sqrt{29}-1)}{2}}$