Question

Simplify
(4th root 9+4th root 4 )^1/3 X (4th root 9-4th root 4)^1/3​

Answer 1

Answer:

So, let’s be wordy for a bit…

What does “the square root of 3 mean”? It means a number (let’s leave to one side whether or not the negative case is included), say x , which when squared (i.e. multiplied by itself) equals 3. So:

x×x=x2=3…(A)

What does “the fourth root of 9 mean”? It means a number (forget about the negative again), say y , which when raised to the fourth power (multiplied by itself four times) equals 9. So:

y×y×y×y=y4=9…(B)

But we know that 3×3=32=9 , so we can write (B) as:

y×y×y×y=3×3

Which we could group up to read:

(y×y)×(y×y)=3×3

Which means that:

y×y=y2=3

So y is the square root of 3 as well. But (again ignoring the negatives) square roots are unique, so x and y are the same number, or:

The square root of 3 is the fourth root of 9 .

Hope that helps and not a fractional power anywhere in sight (even though that would be a lot quicker as pointed out by others).