Question

Fill in the blanks :

vi) $\sqrt[3]{3...}=\sqrt[3]{34}\times \sqrt[3]{35}\times \sqrt[3]{36}$

Answer 1

Step: Fill in the blank

Given: $\sqrt[3]{3...}=\sqrt[3]{34}\times \sqrt[3]{35}\times \sqrt[3]{36}$

$\text{R.H.S}=\sqrt[3]{34}\times \sqrt[3]{35}\times \sqrt[3]{36}$

$=\sqrt[3]{34\times 5\times 6}$ $(\because \sqrt[3]{3a}\times \sqrt[3]{3b}=\sqrt[3]{3a\times b})$

$=\sqrt[3]{3120}$

$\therefore \sqrt[3]{34}\times \sqrt[3]{35}\times \sqrt[3]{36}=\sqrt[3]{3120}$

Hence, the correct answer is $120$.