Question

What is the cube root of 216*512

Answer 1

$\textbf { Hey!! }$

-$\textbf { your answer is -- }$


$\textbf { the cube root of 216*512 is 48 }$

as 216 = 6^3

512 = 8^3

$\textbf { Hope it help you }$

Answer 2

Hey user !!

Here's the answer !!

So let us simplify 216 and 512 to their simplified exponential forms.

We know that 216 = 6 × 6 × 6

Also 512 = 8 × 8 × 8

Hence 216 × 512 = 6³ × 8³

We know the rule that, If bases are different and powers are same then we can take the power as common by multiplying the bases. That is,

aˣ × bˣ = ( ab )ˣ

Hence, 6³ × 8³ = ( 8 × 6 )³ = 48³

Now we need to find the cube root of this number. Hence taking cube root we get,

∛ ( 48³ ) 

Cube root and the power raised to 3 gets cancelled. Hence we are left with 48. 

Hence cube root of 216 × 512 is 48.

Hope my answer helps !!

Cheers !!