Question

simplify the above please ​

Answer 1

Answer:

5^(1/3)

Step-by-step explanation:

Notice that 19 - 2√84 = 7 + 12 - 2√84

= (√7)² + (√12)² - 2√(7)(√12)

= (√12 - √7)²

Therefore,

(19 - 2√84)^(1/6) = (√12- √17)^(2*1/3)

= (√12 - √7)^(1/3) = (2√3 - √7)^(1/3)

Now the question looks like,

= (19 - 2√84)^(1/6) (√7 + 2√3)^(1/3)

= (2√3 - 7)^(1/3) (√7 + 2√3)^(1/3)

= { (2√3 - √7)(2√3 + √7) }^(1/3)

= { (2√3)² - (√7)² }^(1/3)

= (12 - 7)^(1/3)

= 5^(1/3) ≈ 1.709