madisonrichert madisonrichert
  • 24-05-2018
  • Mathematics
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How can you write the expression with the rationalized denominator? ^3 sqrt 7/ ^3 sqrt 49

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Edufirst
Edufirst Edufirst
  • 24-05-2018
Answer: ∛(49) / 7

Explanation:


1) Given expression:

[tex] \frac{ \sqrt[3]{7} }{ \sqrt[3]{49} } [/tex]

2) Notice that 49 = 7².

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

[tex] \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} [/tex]
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