ГДЗ по алгебре 8 класс Макарычев Задание 484

\[\boxed{\text{484\ (484).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

Пояснение.

Решение.

\[\textbf{а)}\ \sqrt{y^{4}} = y^{2}\]

\[\sqrt{y^{4}} = \sqrt{\left( y^{2} \right)^{2}} = \left| y^{2} \right|\text{\ \ }\]

\[y^{2} \geq 0 - при\ любом\ y;\]

\[верно\ при\ y - любое\ число.\]

\[\textbf{б)}\ \sqrt{x^{12}} = x^{6}\]

\[\sqrt{x^{12}} = \sqrt{\left( x^{6} \right)^{2}} = \left| x^{6} \right|\]

\[x^{6} \geq 0 - при\ любом\ x;\]

\[верно\ при\ x - любое\ число.\]

\[\textbf{в)}\ \sqrt{x^{6}} = x^{3}\]

\[\sqrt{x^{6}} = \sqrt{\left( x^{3} \right)^{2}} = \left| x^{3} \right|\]

\[x^{3} \geq 0\ \ при\ x \geq 0;\]

\[верно\ при\ x \geq 0.\]

\[\textbf{г)}\ \sqrt{c^{10}} = - c^{5}\]

\[\sqrt{c^{10}} = \sqrt{\left( c^{5} \right)^{2}} = \left| c^{5} \right|\]

\[c^{5} \leq 0\ \ при\ c \leq 0;\]

\[верно\ при\ c \leq 0.\]

\[\textbf{д)}\ \sqrt{a^{14}} = - a^{7}\]

\[\sqrt{a^{14}} = \sqrt{\left( a^{7} \right)^{2}} = \left| a^{7} \right|\]

\[a^{7} \leq 0\ \ при\ a \leq 0;\]

\[верно\ при\ a \leq 0.\ \]

\[\textbf{е)}\ \sqrt{b^{8}} = b^{4}\text{\ \ }\]

\[\sqrt{b^{8}} = \sqrt{\left( b^{4} \right)^{2}} = \left| b^{4} \right|\]

\[b^{4} \geq 0\ \ при\ любом\ значении\ b;\]

\[верно\ при\ b - любое\ число.\]