Rationalize each denominator

Question

19/ fourth root of 8a

Answer 1

Given function 19 / fourth root of 8a³

19/(8a)^¼

Step1: Determine rationalize factor

8 = 2³.

2 is required.So we neet rationalize with 2^¼

a = a¹.

a³ is required.So we neet rationalize with a^¾

Combined or final rationalize factor is 2^¼a^¾

Step2: Rationalize

= 19/(8a)^¼

= [ 19/(8a)^¼ ] [ 2^¼a^¾ / 2^¼a^¾ ]

= [ 19*2^¼a^¾ / (8a)^¼ 2^¼a^¾ ]

= [ 19*2^¼a^¾ / (2³a¹)^¼ 2^¼a^¾ ]

= [ 19*2^¼a^¾ ] / [ 2^¾ a^¼ 2^¼a^¾ ]

= [ 19*2^¼a^¾ ] / [ 2^¾+¼ a^¼+¾ ]

= [ 19*2^¼a^¾ ] / [ 2¹ a¹ ]

= [ 19*2^¼a^¾ ] / 2a

= (19/2) [2^¼a^¾ / a ]

The solution is 19/(8a)^¼ = (19/2) [2^¼a^¾ / a]