Question

Assume all variables represent non negative numbers . Help please!!

Answer 1

Answer:

A). $2p^{8}$

B). $3m^{7}$

Step-by-step explanation:

A). $\sqrt{4p^{16}}$

    To get the square root of the given expression we will convert it into the square form.

$4p^{16}=(2)^2(p^{8})^2$ [Since 2×2 = 4 and $p^{8}\times p^{8}=p^{16}$]

Therefore, $\sqrt{4p^{16}}=\sqrt{2^{2}\times (p^{8})^2 }$

                             $=2p^{8}$

B). $\sqrt{9m^{44}}$

    Since, $9m^{14}=(3)^2\times (m^7)^2$

    Therefore,  $\sqrt{9m^{44}}=\sqrt{(3)^2\times (m^7)^2}$ [Since 3² = 9 and (m⁷)² = m¹⁴]

                                   $=3m^{7}$