Question

State whether following statement is True or False.

$3\sqrt[4]{4\sqrt[3]{35}}-\sqrt[3]{3\sqrt[4]{45}}$ $=2\cdot \sqrt[12]{125}$

• A. True
• B. False

Answer 1

The correct option is A True

As given $3\sqrt[4]{4\sqrt[3]{35}}-\sqrt[3]{3\sqrt[4]{45}}$

$=3{\left(5^{\frac{1}{3}}\right)}^{\frac{1}{4}}-{\left(5^{\frac{1}{3}}\right)}^{\frac{1}{4}}$

$=3{\left(5\right)}^{\frac{1}{3}\cdot \frac{1}{4}}-{\left(5\right)}^{\frac{1}{3}\cdot \frac{1}{4}}$

$=3\cdot 5^{\frac{1}{12}}-5^{\frac{1}{12}}$

$=2\cdot 5^{\frac{1}{12}}$

$=2\cdot \sqrt[12]{125}$