Question

$\sqrt{30+2\sqrt{29} } -\sqrt{30-2\sqrt{29} }$

Answer 1

$\sqrt{30+2\sqrt{29} }-\sqrt{30-2\sqrt{29} }=\sqrt{29+2\sqrt{29}+1 }-\sqrt{29-2\sqrt{29}+1 } =\\\\=\sqrt{(\sqrt{29})^{2}+2\sqrt{29}+1^{2}}-\sqrt{(\sqrt{29})^{2}-2\sqrt{29}+1^{2}}=\\\\=\sqrt{(\sqrt{29}+1)^{2}} -\sqrt{(\sqrt{29}-1)^{2}}=|\sqrt{29}+1|-|\sqrt{29}-1|=\\\\=\sqrt{29} +1-\sqrt{29} +1=\boxed2$