Question

Hellpppp plz quickly

Answer 1

$8 < \sqrt[3]{a} < 9$
$512 < a < 729$

So, a can be any number between (512, 729).
∴ answer is (A) 679

Answer 2

8 < ∛a < 9
We need to solve for a.
Let's get the 1/3th root of the whole equation:
$\sqrt[1/3]{8} \ \textless \ \sqrt[1/3]{cubic-root-of-x} \ \textless \ \sqrt[1/3]{9}$


$\sqrt[1/3]{cubic-root-of-x} = x$
$\sqrt[1/3]{8} = 512$
$\sqrt[1/3]{9} = 712$

So
$\sqrt[1/3]{8} \ \textless \ \sqrt[1/3]{cubic-root-of-x} \ \textless \ \sqrt[1/3]{9}$

512 < x < 729

Now from the values we got, 679 is between 512 and 729.

So  8 < ∛679 < 9 (∛679 ≈ 8.78) (Answer A)


Hope this helps! :D