Question

Simplify : 3 cube root 40 4 cube root 320 cube root 5

Answer 1

We have:
3∛40 × 4∛320 × √5

40 can be written as 2 x 2 x 2 x 5
320 can be written as 2 x 2 x 2 x 2 x 2 x 2 x 5

Taking everything (except √5) within the ∛ sign, we get:
(∛2 x 2 x 2 x 5 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 3 x 3 x 3 x 4 x 4 x 4) x √5

(2 x 2 x2 x 3 x 4) x ∛25 x √5
96 x ∛25 x √5  ------------------------- (i)

∛25 can also be written as $5^{2/3}$
√5 can also be written as $5^{1/2}$

So we can rewrite (i) as :

96 x  ($5^{2/3+1/2}$)
96 x $5^{7/6}$

We can further simplify this as:
96 x  ($5^{6/6+1/6}$)
96 x 5 x $5^{1/6}$
480 x $5^{1/6}$

Answer 2

Answer:

HEY MATE!  I HOPE IT WILL HELP U !!

Step-by-step explanation:

We have:

3∛40 × 4∛320 × √5

40 can be written as 2 x 2 x 2 x 5

320 can be written as 2 x 2 x 2 x 2 x 2 x 2 x 5

Taking everything (except √5) within the ∛ sign, we get:

(∛2 x 2 x 2 x 5 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 3 x 3 x 3 x 4 x 4 x 4) x √5

(2 x 2 x2 x 3 x 4) x ∛25 x √5

96 x ∛25 x √5  ------------------------- (i)

∛25 can also be written as

√5 can also be written as

So we can rewrite (i) as :

96 x  ()

96 x

We can further simplify this as:

96 x  ()

96 x 5 x

480 x