Question

Simplify: sqrt 60a^8 over sqrt 72a^5

Answer 1

\[\frac{\sqrt{60a^8}}{\sqrt{72a^5}} = \sqrt{\frac{60a^8}{72a^5}}\]

now you can simplify things \[\sqrt{\frac{5a^3}{6}}\]

which can be simplifed further.

by looking at a^3 = a^2 x a

Answer 2

did you get the answer ?

Answer 3

not exactly. The back of the book is telling me the answer is supposed to be: |a|/6 sqrt 30a and I'm not seeing where they get that from

Answer 4

well it can be simplifed further by looking at a^3\[\sqrt{\frac{5}{6} \times a^2 \times a}\]

a^2 can be taken outside the radical

so it becomes

\[\sqrt{\frac{5}{6}a} \times \sqrt{a^2} = a \sqrt{\frac{5a}{6}}\]

as per the back of the book.

Answer 5

so then how is the book saying it should also have the square root of 30 in the answer?

Answer 6

but what the back of the book has done is this

\[\frac{\sqrt{60a^8}}{\sqrt{72a^5}} = \frac{\sqrt{60a^8}}{\sqrt{36}\times \sqrt{2a^5} }\]

Answer 7

ohh okay thanks! :)

Answer 8

then thay have said

\[\frac{1}{\sqrt{36}} \times \sqrt \frac{60a^8}{2a^5}\]

this becomes

\[\frac{1}{6} \times \sqrt{30a^3} \]

which will become

\[\frac{a}{6} \sqrt{30a}\]