Question

find the rationalising factor of cube root 72

Answer 1

The rationalizing factor of cube root 72 is 4.1602.

Explanation:

• Cube root is where a number is multiplied three times.
• Cube root is represented as $a^{3}$, where a can be any value.
• For example, $5^{3}$ = 125. So Cube root of 125 is, $\sqrt[3]{125} = 5$.
• Similarly cube root of 72,

                   $\sqrt[3]{72} = \sqrt[3]{2X2X2X3X3}$

                           $= \sqrt[3]{3X3}$ × 2

                           $= 2.0801$ × 2

                    $\sqrt[3]{72} = 4.1602$.

• Hence  the rationalizing factor of cube root 72 is 4.1602.

Answer 2

The rationalising factor of $\sf \sqrt[3]{72}$ is $\sf \sqrt[3]{3}$

Given : The number $\sf \sqrt[3]{72}$

To find : The rationalising factor

Solution :

Here the given number is

$\sf \sqrt[3]{72}$

The number under the radical sign is 72

We factorise the number under the radical sign

72 = 2 × 2 × 2 × 3 × 3

$\displaystyle \sf{ \implies 72 = {2}^{3} \times {3}^{2} }$

We see that the factor 2 is triplet form but 3 is in pair form

We need one more 3 to make 3 in triplet form so that the new number obtained is perfect cube

Hence the required rationalising factor is $\sf \sqrt[3]{3}$

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