Question

Simplify and/or solve (please show work)
1.) 3√24+4√54 = ?

2.)5√54 - 2√6 = ?

3.) 5√x = √10x+60 = ? (solve for x)

Answer 1

1) \(\Large 3\sqrt{24}+4\sqrt{54}=3\sqrt{4\times 6}+4\sqrt{9\times 6} \\\Large =3\times 2\sqrt{6} + 4\times 3\sqrt{6} =6\sqrt{6}+12\sqrt{6}=\huge 18\sqrt{6} \)

2) \(\Large 5\sqrt{54} - 2\sqrt{6}=5\sqrt{9\times 6}-2\sqrt{6}\\ \Large =5\times 3\sqrt{6} -2\sqrt{6}=15\sqrt{6}-2\sqrt{6}=\huge 13\sqrt{6}\)

3) \(\Large 5\sqrt{x} = \sqrt{10x+60} \Rightarrow (5\sqrt{x})^2=(\sqrt{10x+60})^2\\\Large \Leftrightarrow 25x=10x+60 \Leftrightarrow 25x-10x=60 \\\Large \Leftrightarrow 15x=60 \Leftrightarrow x=\frac{60}{15}=\huge 4\)