Question

Show that:

(ii) $\sqrt[3]{364}\times \sqrt[3]{3729}=\sqrt[3]{364\times 729}$

Answer 1

Step: Prove that: $\sqrt[3]{364}\times \sqrt[3]{3729}=\sqrt[3]{364\times 729}$

Given: $\sqrt[3]{364}\times \sqrt[3]{3729}=\sqrt[3]{364\times 729}$

L.H.S.=$\sqrt[3]{364}\times \sqrt[3]{3729}$

$=\sqrt[3]{34\times 4\times 4}\times \sqrt[3]{39\times 9\times 9}$

$=4\times 9$

$=36$
Now, R.H.S.$=\sqrt[3]{364}\times \sqrt[3]{3729}$

$=\sqrt[3]{34\times 4\times 4\times 9\times 9\times 9}$

$=4\times 9$

$=36$

$\because L.H.S.=R.H.S.$

$\therefore \sqrt[3]{364}\times \sqrt[3]{3729}=\sqrt[3]{364\times 729}$

Hence proved.