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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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Other answers:

@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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