Question

simplify by combining similar terms:
$\sqrt[3]{625 } + \sqrt[3]{40} + \sqrt[3]{135}$
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Answer 1

Answer:

Hey there !!!!!

=2∛40+3∛625-4∛320-----Equation 1

We can write

40=2*2*2*5=2³*5

∛40=∛(2³*5)= ∛2³*∛5=2∛5

625=25²=(5²)²

∛625=∛5⁴=5∛5

320=40*8=40*2³=4*2³*10=2²*2³*2*5=2⁶*5

∛320=∛2⁶*5=(2⁶)¹/₃*∛5=2²*∛5=4*∛5

So, ∛40 =2*∛5 ,∛625=5∛5 ,∛320=4∛5

Now substituting values of ∛40,∛625 and ∛320 in equation 1

2∛40+3∛625-4∛320 = 2*2∛5+3*5*∛5-4*4∛5

=4∛5+15∛5-16∛5

=∛5(19-16) = 3∛5

Hope this helped you !!!

Step-by-step explanation:

Answer 2

Answer:

$\sqrt[3]{625} = \sqrt[3]{125 \times 5} \\ 5 \sqrt[3]{5} \\ \sqrt[3]{40} = \sqrt[3]{8 \times 5} \\ 2 \sqrt[3]{5} \\ \sqrt[3]{135} = \sqrt[3]{27 \times 5} \\ 3 \sqrt[3]{5}$

Step-by-step explanation:

Therefore the answer is

$5 \sqrt[3]{5} + 2 \sqrt[3]{5} + 3 \sqrt[3]{5} = 10 \sqrt[3]{5}$