ho0w did -3/2root3 turned in to -root 3/2
To convert -3/2√3 to -√3/2, we can rationalize the denominator.
Multiplying the numerator and denominator by √3, we get:
-3/2√3 * √3/√3 = -3√3 / 2√(3*3) = -3√3 / 2√9 = -3√3 / 2*3 = -√3/2.
Therefore, -3/2√3 is equivalent to -√3/2.
To understand how -3/2√3 can be simplified to -√3/2, follow the steps below:
Step 1: Start with the expression -3/2√3.
Step 2: Rationalize the denominator by multiplying both the numerator and denominator by √3. This will eliminate the square root in the denominator.
(-3/2√3) x (√3/√3) = (-3√3)/(2√9)
Step 3: Simplify the denominator √9 to 3.
(-3√3)/(2√9) = (-3√3)/(2√3 x √3) = (-3√3)/(2 x 3)
Step 4: Further simplify.
(-3√3)/(2 x 3) = -√3/2
Therefore, -3/2√3 simplifies to -√3/2.
To understand how -3/2√3 can be simplified to -√3/2, we need to simplify the expression step by step.
1. Start with -3/2√3.
2. We can simplify the expression by multiplying both the numerator and denominator by √3. This is called rationalizing the denominator.
(Note: When multiplying a square root expression with its conjugate, the result will be a rational number.)
-3/2√3 * √3/√3 = -3√3/2√(3 * 3)
Simplifying the denominator gives: -3√3/2√9 = -3√3/2√9
3. Since the square root of 9 is a rational number (3), we can simplify further:
-3√3/2 * 3 = -3√3/2 * 3/3
Simplifying the numerator gives: -3√3/6
4. Finally, we can divide both the numerator and the denominator by 3 to simplify further:
-3√3/6 = -(√3/2)
Simplifying the expression gives: -√3/2.
So, -3/2√3 can be simplified to -√3/2.