This question combines the concepts of converting a whole radical to a mixed radical and only radicals that are the 'same' can be added or subtracted.
Each number inside the radical needs to be factored so that one of the factors is a perfect square and thus can be taken outside the radical. look for perfect squares of 4, 9, 16 and perfect cubes of 8, 27, 64
sqr ((9 x 2)t^3) + cubrt((64 x 2)) - cubrt ((8 x 2)) + t sqr ((16 x 2)t) also know that sqr (t^3) = t sqr (t) by taking out the perfect square t^2
(3t)sqr ((2)t) + (4)cubrt((2)) - (2)cubrt ((2)) + (4t) sqr ((2)t) The 1st term and the 4th term have the same variable and radical so they can be combined and the 2nd and 3rd terms have the same radical so they can be combined. For ease we can change the order.
(3t)sqr ((2)t) +(4t) sqr ((2)t) + (4)cubrt((2)) - (2)cubrt ((2)) After combining like terms the result will be ...
1 year ago
Answered By Albert S
sqr (18t^3) + cubrt(128) - cubrt (16) + t sqr (32t)
This question combines the concepts of converting a whole radical to a mixed radical and only radicals that are the 'same' can be added or subtracted.
Each number inside the radical needs to be factored so that one of the factors is a perfect square and thus can be taken outside the radical. look for perfect squares of 4, 9, 16 and perfect cubes of 8, 27, 64
sqr ((9 x 2)t^3) + cubrt((64 x 2)) - cubrt ((8 x 2)) + t sqr ((16 x 2)t) also know that sqr (t^3) = t sqr (t) by taking out the perfect square t^2
(3t)sqr ((2)t) + (4)cubrt((2)) - (2)cubrt ((2)) + (4t) sqr ((2)t) The 1st term and the 4th term have the same variable and radical so they can be combined and the 2nd and 3rd terms have the same radical so they can be combined. For ease we can change the order.
(3t)sqr ((2)t) + (4t) sqr ((2)t) + (4)cubrt((2)) - (2)cubrt ((2)) After combining like terms the result will be ...
(7t) sqr ((2)t) + (2)cubrt((2))