Question

Which monomial is a perfect cube? 49p9q3r24 81p12q15r12 121p9q3r6 343p6q21r6.

Answer 1

The monomial is a perfect cube is $\rm 343p^6q^{21}r^6$.

Perfect cubes;

Perfect cubes are the numbers that are the triple product of the same number.

We have to determine

Which monomial is a perfect cube?

A perfect cube monomial must have three identical roots, such that the product of the roots equals the perfect square monomial.

It must be possible for the coefficient of a perfect cube monomial to be written in the form n3, where n equals the cube root of the coefficient.

A perfect cube monomial must have exponents on the variables.

Then

The monomial is a perfect cube is;

$\rm= 343p^6q^{21}r^6\\\\= \sqrt[3]{ 343 }= 7$

Hence, the monomial is a perfect cube is $\rm 343p^6q^{21}r^6$.

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