Simplify the following :

1.	Simplify the following :
Answer» $\huge \fbox \orange{Solutions:}$ $1. \: \sqrt{45} - 3 \sqrt{20} + 4√5$ $\sf \colorbox{pink} {<klux>ANSWER</klux>. 1}$ $\sqrt{45} - 3 \sqrt{20} + 4√5$ $= \sqrt{3 \times 3 \times 5} - 3 \sqrt{2 \times 2 \times 5} + 4 \sqrt{5}$ $= 3 \sqrt{5} - 3 \times 2 \sqrt{5} + 4 \sqrt{5}$ $= 3 \sqrt{5} - 6 \sqrt{5} + 4 \sqrt{5}$ $= 7 \sqrt{5} - 6 \sqrt{5}$ $= \sqrt{5}$ $2. \: \frac{ \sqrt{24} }{8} + \frac{ \sqrt{54} }{9}$ $\sf \colorbox{pink} {Answer. 2}$ $\textbf{Given:} \frac{ \sqrt{24} }{8} + \frac{ \sqrt{54} }{9}$ SOLUTION: $= \frac{ \sqrt{24} }{8} + \frac{ \sqrt{54} }{9}$ $= \frac{ \sqrt{2 \times 2 \times 2 \times 3} }{8} + \frac{ \sqrt{2 \times 3 \times 3} }{9}$ $⇒ \frac{2 \sqrt{2 \times 3} }{8} + \frac{3 \sqrt{2 \times 3} }{9} = \frac{ \sqrt{6} }{4} + \frac{ \sqrt{6} }{3}$ $⇒ \sqrt{6} \left( \frac{1}{4} + \frac{1}{3} \right) \] = \sqrt{6} \times \frac{7}{12}$ $= \frac{7}{12} \sqrt{6}$ $3. \: \: \sqrt{3} - 2 \sqrt{27} + \frac{7}{ \sqrt{3} }$ $\sf \colorbox{pink} {Answer. 3}$ $\textbf{Given:} \sqrt{3} - 2 \sqrt{27} + \frac{7}{ \sqrt{3} }$ Solution: $⇒3 \sqrt{3} - 2 \sqrt{27} + \frac{7}{ \sqrt{3} }$ $⇒3 \sqrt{3 } - 6 \sqrt{3} + \frac{7}{ \sqrt{3} }$ $⇒9 \sqrt{3} - \frac{7}{ \sqrt{3} } = \left( \frac{9 \sqrt{3} }{ \sqrt{3} } \times \sqrt{3} \right) \] + \frac{7}{3}$ $⇒ \frac{27}{ \sqrt{3} } + \frac{7}{ \sqrt{3} } = \frac{34}{ \sqrt{3} }$ $4. \: \sqrt[4]{81} - 8 \sqrt[3]{216} + 15 \sqrt[5]{32} + \sqrt{225}$ $\sf \colorbox{pink} {Answer .4 }$ $\textbf{Given:} \sqrt[4]{81} - 8 \sqrt[3]{216} + 15 \sqrt[5]{32} + \sqrt{225}$ Solution: $= \sqrt[4]{ {3}^{4} } - 8$ $= \sqrt[3]{ {6}^{3} } + 15$ $= \sqrt[5]{ {2}^{5} } + \sqrt{ {15}^{2} }$ $= 3 - 8 \times 6 + 15 \times 2 + 15$ $= 3 - 48 + 30 + 15 = 0$ $\\ \\ \\$ ‣Please do not report if the answer is WRONG, we have tried our BEST to give you the correct answer $\\ \\ \\ \\ \\ \\ \\ \sf \colorbox{gold} {\red(ANSWER ᵇʸ ⁿᵃʷᵃᵇ⁰⁰⁰⁸}$

Answer»

$\huge \fbox \orange{Solutions:}$