Question

rationalizing a denominator
the process for rationalizing a denominator in a variable expression is the same as in a numeric expression. heres a real - world example.
the kinetic energy of the car of a rollercoaster is given by the formula ( k=\frac{1}{2}mv^{2} ), where ( k ) is kinetic energy, ( m ) is the mass of the car, and ( v ) is the velocity of the car. solving this formula for ( v ), we get ( v = sqrt{\frac{2k}{m}} ).
which formula gives the velocity of the car in simplest form?
( v=\frac{sqrt{2km}}{m} )
( v=\frac{sqrt{2k}}{m} )
( v=\frac{sqrt{2km}}{2m} )

Explanation:

Step1: Aplicar la regla de la raíz cuadrada de una fracción

$$\sqrt{\frac{2k}{m}}=\frac{\sqrt{2k}}{\sqrt{m}}$$

Step2: Racionalizar el denominador

Multiplicar numerador y denominador por $\sqrt{m}$:
$$\frac{\sqrt{2k}}{\sqrt{m}}\times\frac{\sqrt{m}}{\sqrt{m}}=\frac{\sqrt{2k\times m}}{m}=\frac{\sqrt{2km}}{m}$$

Answer:

$v = \frac{\sqrt{2km}}{m}$