Задание 14, стр 26

Question

Сравните.

$$	ext{1) $\sqrt{5}+\sqrt{5} \bigcirc \sqrt{20}\quad$ 2) $\sqrt{18}+\sqrt{8} \bigcirc \sqrt{54}\quad$ 3) $\sqrt{63}+\sqrt{28} \bigcirc \sqrt{168}$}$$ 
$$	ext{4) $\sqrt{200}+\sqrt{200} \bigcirc \sqrt{400}\quad$ 5) $5 \sqrt{27}-2 \sqrt{48} \bigcirc 9 \sqrt{2}$}$$

Gimli · Accepted Answer

$$ \begin{align*} ext{1) } \sqrt{5}+\sqrt{5}&\bigcirc \sqrt{20}\qquad \quad & ext{2)}&\sqrt{18}+\sqrt{8}&\bigcirc \sqrt{54}\ 2\sqrt{5}&\bigcirc \sqrt{20}&&\sqrt{2}(\sqrt{9}+\sqrt{4})&\bigcirc \sqrt{54}\ \sqrt{4\cdot 5}&\bigcirc \sqrt{20}&&\sqrt{2}(3+2)&\bigcirc \sqrt{54}\ \sqrt{20}&=\sqrt{20}&&5\sqrt{2}&\bigcirc \sqrt{54}\ &&&\sqrt{25}\cdot \sqrt{2}&\bigcirc \sqrt{54}\ &&& \sqrt{50}&<\sqrt{54} \end{align*} $$ $$ \begin{aligned} ext { 3) }& \sqrt{63}+\sqrt{28} \bigcirc \sqrt{168} & 4) \sqrt{200}+\sqrt{200} &\bigcirc \sqrt{400} \ &\sqrt{7}(\sqrt{9}+\sqrt{4}) \bigcirc \sqrt{368} & 2 \sqrt{200} &\bigcirc \sqrt{400} \ &\sqrt{7}(3+2) \bigcirc \sqrt{168} & \sqrt{4 \cdot 200} &\bigcirc \sqrt{400} \ &5 \sqrt{7} \bigcirc \sqrt{168} &\sqrt{800} & >\sqrt{400} \ &\sqrt{257} \bigcirc \sqrt{168} & & \ &\sqrt{175}>\sqrt{168} & &\ ext { 5) } &5 \sqrt{27}-2 \sqrt{48} \bigcirc 9 \sqrt{2}\ &\sqrt{3}(5 \sqrt{9}-2 \sqrt{16}) \bigcirc 9 \sqrt{2}\ &\sqrt{3}(5\cdot 3-24) \bigcirc 9 \sqrt{2}\ & \sqrt{3}\cdot 7 \bigcirc 9 \sqrt{2} \ &\sqrt{3\cdot 49} \bigcirc \sqrt{81 \cdot 2} \ &\sqrt{147} <\sqrt{362} \end{aligned} $$

Задание 14, стр 26

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Задание 14, стр 26

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