Question

√45k^7q^8

Answer 1

\[\sqrt{9(5)k ^{6}kq ^{8}}\]

Answer 2

Rewrite it like that and then take the square root of all the perfect square factors.

Answer 3

\[\large\sqrt{45 k^7 q^8}\]

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.

Answer 4

@Mertsj am I wrong somewhere ...... ?

Answer 5

\[3k^3q^4\sqrt{5k}\]

Answer 6

\[\large \cfrac{3k^4 q^4 \sqrt{5}}{\sqrt{k}}\]

\[\large \cfrac {3k^4 q^4 \sqrt{5}*\sqrt{k}}{\sqrt{k}*\sqrt{k}}\]

\[\large 3k^3 q^4 \sqrt{5k}\]

Yours method is easier @Mertsj gud work