Question

Сравните числа 1)4√3 и 3√8 2)4*√15/8и 1/5√750

Answer 1

1)$4 \sqrt{3}\ \textgreater \ 3 \sqrt{8}$, т.к.
   $\\ 4\sqrt{3} = \sqrt{16*3} = \sqrt48} \\ 3 \sqrt{8} = \sqrt{9*8} =\sqrt{72}$
2)$\\ 4 \sqrt{ \frac{15}{8} } = \frac{1}{5} \sqrt{750}$, т.к.
   $4 \sqrt{ \frac{15}{8} } = \sqrt{ \frac{16*15}{8} } = \sqrt{2*15} = \sqrt{30} \\ \frac{1}{5} \sqrt{750} = \frac{1}{5} \sqrt{5^{2} *30} = \frac{1}{5} *5* \sqrt{30} = \sqrt{30}$