Question

Сравните 2 корня из 6 и 4 корня из 2

Answer 1

Возведи в квадрат, два корня из шести будет равно двадцати четырём, а четыре корня из двух будет равно тридцати двум. 32>24. Следовательно , четыре корня из двух больше

Answer 2

4 корня из 2 больше чем 2 корня из 6

Answer 3

I can understand and communicate in Russian. To compare $2\sqrt{6}$ and $4\sqrt{2}$, we can use the property of radicals that $\sqrt{ab}=\sqrt{a}\sqrt{b}$. Therefore, we can rewrite $2\sqrt{6}$ as $2\sqrt{2}\sqrt{3}$ and $4\sqrt{2}$ as $4\sqrt{2}\sqrt{1}$. Then, we can compare the coefficients of $\sqrt{2}$ and the values under the radicals. We see that $2<4$ and $\sqrt{3}>\sqrt{1}$, so we cannot conclude which expression is larger without further simplification. To do that, we can approximate the values of $\sqrt{3}$ and $\sqrt{2}$ using a calculator or a table of square roots. We get $\sqrt{3}\approx 1.732$ and $\sqrt{2}\approx 1.414$. Multiplying these values by the coefficients, we get $2\sqrt{6}\approx 4.899$ and $4\sqrt{2}\approx 5.657$. Therefore, we can conclude that $2\sqrt{6}<4\sqrt{2}$. For more information, you can visit [this website](https://ru.symbolab.com/solver/roots-calculator) or [this website](https://okcalc.com/ru/root/).