Add or subtract the radical expressions as indicated, if possible. $$\sqrt [ 5 ] { 15 } + 8 \sqrt [ 5 ] { 15 } - \sqrt [ 5 ] { 7 }$$
A) $8 \sqrt [ 5 ] { 23 }$
B) $9 \sqrt [ 5 ] { 15 } - \sqrt [ 5 ] { 7 }$
C) $8 \sqrt [ 5 ] { 8 }$
D) Cannot be simplified further

Question

Quizplus · Accepted Answer

Radical expressions can be added or subtracted only if they have the same index and radicand. Here, $\sqrt [ 5 ] { 15 }$ and $8 \sqrt [ 5 ] { 15 }$ can be combined because they have the same index (5) and radicand (15), resulting in $9 \sqrt [ 5 ] { 15 }$. The term $\sqrt [ 5 ] { 7 }$ cannot be combined with the others because it has a different radicand, so the simplified expression is $9 \sqrt [ 5 ] { 15 } - \sqrt [ 5 ] { 7 }$.

Add or Subtract the Radical Expressions as Indicated, If Possible 155+8155−75\sqrt [ 5 ] { 15 } + 8 \sqrt [ 5 ] { 15 } - \sqrt [ 5 ] { 7 }515​+8515​−57​

Add or Subtract the Radical Expressions as Indicated, If Possible $\sqrt [ 5 ] { 15 } + 8 \sqrt [ 5 ] { 15 } - \sqrt [ 5 ] { 7 }$