Question

How do I simplify the expression \[\sqrt {{{\left( {a + 2} \right)}^2}} \]?

Answer 1

Hint: In the given question, we have been given an algebraic expression. It is clearly a square inside a square root bracket. We are going to solve it by changing the square root bracket into a power and then applying the product rule of powers to solve it.

Formula Used:
We are going to use the product rule of powers formula:
\[{\left( {{a^m}} \right)^n} = {a^{m \times n}}\]

Complete step-by-step answer:
We have to simplify the value of \[\sqrt {{{\left( {a + 2} \right)}^2}} \].
We are going to use the product rule of powers formula:
\[{\left( {{a^m}} \right)^n} = {a^{m \times n}}\]
Now, \[\sqrt {{{\left( {a + 2} \right)}^2}} = {\left( {{{\left( {a + 2} \right)}^2}} \right)^{\dfrac{1}{2}}}\]
Substituting the value of \[m = \dfrac{1}{2}\] and \[n = 2\], we get,
\[\sqrt {{{\left( {a + 2} \right)}^2}} = {\left( {a + 2} \right)^{{2} \times \dfrac{1}{{{2}}}}} = \left( {a + 2} \right)\]

Note: In the given question, we simply had to put the formula of product rule of powers. Then we just substituted the values, simplified the result and we got our answer. So, it is really important that we know the formulae and where, when and how to use them so that we can get the correct result.