To simplify the given expression, we can first rewrite the radical as a quotient of two radicals.
sqrt(32/t^4)=sqrt(32)/sqrt(t^4)
Now, we can rationalize the denominator of the quotient. In order to do that, we need a perfect square inside the square root. The variable t in the denominator has an even exponent, so we can rewrite the exponent as the product of two identical integer exponents.
sqrt(32)/sqrt(t^4) ⇒ sqrt(32)/sqrt(t^(2* 2))
Let's start by finding the exponents necessary to create perfect squares in the denominator. Our goal is to have two of each factor.
Now that we have found the factor that will make the radicand of the denominator perfect square only, we can begin to simplify the quotient. While simplifying, we should consider the index of the radicals to see how we should format our solution.
sqrt(a^n)=
a if n is odd
|a| if n is even
Because our radical has an even root and the variable has an even exponent, we will need to use absolute value symbols to simplify our expression.
