√45k^7q^8

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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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\[\sqrt{9(5)k ^{6}kq ^{8}}\]
Rewrite it like that and then take the square root of all the perfect square factors.
\[\large\sqrt{45 k^7 q^8}\] Now , \[\large k^7 = \cfrac{k^7 * \color {red}k}{\color {green}k} = \cfrac{k^8}{k}\] also, \[\large\sqrt{k^8} = k^4\] and \[\large \sqrt{q^8} = q^4\] and \[\large \sqrt{45} = \sqrt{9*5} = \sqrt{9}\sqrt{5} = 3\sqrt{5}\] Now you can put all the values in the question \[\large\sqrt{45 k^7 q^8}\] \[\large \color {green}{\sqrt{45}} * \color {red}{\sqrt{k^7}} * \color {brown}{\sqrt{q^8}}\] we have already calculated \[\large \sqrt{45}\] \[\large \sqrt{q^8}\] and how to change \(\large k^7\) into \(\large \cfrac{k^8}{k}\) also we have find out \[\large\sqrt{k^8}\] You can solve it further also the way shown by @Mertsj is a lot easier you can use either of them.

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@Mertsj am I wrong somewhere ...... ?
\[3k^3q^4\sqrt{5k}\]
\[\large \cfrac{3k^4 q^4 \sqrt{5}}{\sqrt{k}}\] \[\large \cfrac {3k^4 q^4 \sqrt{5}*\sqrt{k}}{\sqrt{k}*\sqrt{k}}\] \[\large 3k^3 q^4 \sqrt{5k}\] Yours method is easier @Mertsj gud work

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