Question

What is the monomial if a square of a monomial is: 1/4 a2n

Answer 1

Answer:

$\frac{1}{2} a^n$

Step-by-step explanation:

Square of the monomial is $\frac{1}{4}a^{2n}$

To get the monomial we take square root

Lets take square root for each term

$\sqrt{\frac{1}{4}a^{2n}}$

$\sqrt{\frac{1}{4}}=\fract{1}{2}$ because square root of 4 is 2

$\sqrt{a^{2n}}=(a^{2n})^\frac{1}{2}$

2/2 is 1 so, its a^n

Required monomial is  $\frac{1}{2} a^n$

Answer 2

Answer:

$\frac{1}{2}a^n$

Step-by-step explanation:

Givens:

• Square of a monomial: $\frac{1}{4} a^{2n}$.

The problem is asking for the monomial, and the given is squared. What we have to do is to extract that square from expression, and that it's done applying a squared root, because that's the opposite operation of a squared power:

$\sqrt{\frac{1}{4} a^{2n}}$

So, here we have to find the squared root of $\frac{1}{4}$ and $a^{2n}$, applying the root to each factor:

$\sqrt{\frac{1}{4}} \sqrt{a^{2n}}$

So, we know that a root can be expressed as a fractional exponent, and also the root of a fraction is the root of each part of the fraction:

$\frac{\sqrt{1}}{\sqrt{4}} (a^{2n})^{\frac{1}{2} }$

Now, we solve:

$\frac{1}{2}a^{\frac{2n}{2}}= \frac{1}{2}a^n$

Therefore, the monomial expression is $\frac{1}{2}a^n$