Question

How can you write the expression with the rationalized denominator? ^3 sqrt 7/ ^3 sqrt 49

Answer 1

Answer: ∛(49) / 7

Explanation:


1) Given expression:

$\frac{ \sqrt[3]{7} }{ \sqrt[3]{49} }$

2) Notice that 49 = 7².

3) With that in mind, rationalize by multiplying numerator and denominator by ∛7:

$\frac{ \sqrt[3]{7} }{ \sqrt[3]{49} } \frac{ \sqrt[3]{7} }{ \sqrt[3]{7} } = \frac{ \sqrt[]{7^2} }{ \sqrt[3]{7^3} } = \frac{ \sqrt[3]{49} }{7}$