Question

What is the monomial if a square of a monomial is: 0.0001a^8x^4 and 9/25a^2n+4

Answer 1

`A = 0.01a^(4)x^(2)` and
`A = - 0.01a^(4)x^(2)`

`B = (3)/(5) a^(n + 2)` and
`B = - (3)/(5) a^(n + 2)`

Explanation:

If the square of monomials is given by the given expressions then we have to find the monomials.

Let,
`A^(2) = 0.0001 a^(8)x^(4) = (0.01)^(2)(a^(4))^(2)(x^(2) )^(2) = [0.01a^(4)x^(2)]^(2)`

⇒
`A = 0.01a^(4)x^(2)` and
`A = - 0.01a^(4)x^(2)`

{Square root both sides}

Again, let
`B^(2) = (9)/(25)a^((2n + 4)) = (3^(2) )/(5^(2)) a^(2(n + 2)) = [(3)/(5)a^(n + 2)  ]^(2)`

⇒
`B = (3)/(5) a^(n + 2)` and
`B = - (3)/(5) a^(n + 2)`

{Square root both sides} (Answer)