Question

Simplify!
5/√(5-2√6)

Answer 1

`5-2√(6)}=√(3)^2-2√(3)√(2)+√(2)^2=(√(3)-√(2))^2`

Hence
`\frac{1}{\sqrt{5-2√(6)}}}=(1)/(√(3)-√(2))=(\sqrt3+\sqrt2)/(\sqrt3^2-\sqrt2^2)=\sqrt3+\sqrt2`

Therefore
`\boxed{(5)/(√(5-2\sqrt6))=5(\sqrt3+\sqrt2)}`

Answer 2

`\frac{5}{\sqrt{5-2√(6)}}^{(\sqrt{5+2√(6)}}= \frac{5\sqrt{5+2√(6)}}{\sqrt{(5-2√(6))(5+2√(6))}}= \\\\\\ = \frac{5\sqrt{5+2√(5)}}{√(25-24)}= \\\\ = \frac{5\sqrt{5+2√(6)}}{1}= \\\\ =\boxed{5\sqrt{5+2√(6)}}`



`5\sqrt{5+√(24)}= \\\\ A=5 \\ B=24 \\ C^2=A^2-B= 25-24=1 \ \ \ \Longrightarrow \boxed{C=1} \\\\\\ 5\sqrt{(A+C)/(2)+(A-C)/(2)}= 5\sqrt{(5+1)/(2)+(5-1)/(2)}= \\\\=5 \sqrt{(6)/(2)+(4)/(2)}= \\\\ =\boxed{\boxed{5(√(3)+√(2))}}`