Simplify:Remember to use absolute value notation when necessary. If a root cannot be simplified, state this.
Ques: 5sq.rt-1/32
To simplify the expression 5√(-1/32), let's break it down step by step.
Step 1: Simplify the fraction inside the square root.
The expression can be written as 5√(-1)/(√32). Let's simplify the fraction -1/32 first.
The square root of -1 is denoted as "i", which represents the imaginary unit. Therefore, we can rewrite √(-1) as √(-1) = i.
Now, let's simplify the fraction. The square root of 32 can be broken down into the square root of 16 multiplied by the square root of 2. Simplifying further, we have √32 = √(16 * 2) = √16 * √2 = 4√2.
Substituting these values, we obtain 5i/(4√2).
Step 2: Rationalize the denominator.
Since the denominator contains a square root (√2), we need to rationalize it by multiplying both the numerator and denominator by the conjugate of the denominator.
The conjugate of √2 is -√2, so we should multiply both the numerator and denominator by (-√2).
(5i/(4√2)) * ((-√2)/(-√2))
Simplifying this, we get -5i√2/8.
Therefore, the simplified expression is -5i√2/8.