Question

-81)x^{2} }" align="absmiddle" class="latex-formula">

Answer 1

Answer:

We conclude that:

$\sqrt{\left(-81\right)x^2}=9ix$

Step-by-step explanation:

Given the radical expression

$\sqrt{\left(-81\right)x^2}$

simplifying the expression

$\sqrt{\left(-81\right)x^2}$

Remove parentheses:  (-a) = -a

$\sqrt{\left(-81\right)x^2}=\sqrt{-81x^2}$

Apply radical rule:   $\sqrt{-a}=\sqrt{-1}\sqrt{a},\:\quad \mathrm{\:assuming\:}a\ge 0$

                 $=\sqrt{-1}\sqrt{81x^2}$

Apply imaginary number rule:  $\sqrt{-1}=i$

                 $=i\sqrt{81x^2}$

Apply radical rule:   $\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b},\:\quad \mathrm{\:assuming\:}a\ge 0,\:b\ge 0$

                  $=\sqrt{81}i\sqrt{x^2}$

                  $=9i\sqrt{x^2}$

Apply radical rule:  $\sqrt[n]{a^n}=a,\:\quad \mathrm{\:assuming\:}a\ge 0$

                  $=9ix$

Therefore, we conclude that:

$\sqrt{\left(-81\right)x^2}=9ix$