Asked by edfe

What is the simplified form of the following expression? Assume x greater-than-or-equal-to 0 and y greater-than-or-equal-to 0

2 (RootIndex 4 StartRoot 16 x EndRoot) minus 2 (RootIndex 4 StartRoot 2 y EndRoot) + 3 (RootIndex 4 StartRoot 81 x EndRoot) minus 4 (RootIndex 4 StartRoot 32 y EndRoot)
5 (RootIndex 4 StartRoot x EndRoot) minus 4 (RootIndex 4 StartRoot 32 y EndRoot)
5 (RootIndex 4 StartRoot x EndRoot) minus 6 (RootIndex 4 StartRoot 2 y EndRoot)
13 (RootIndex 4 StartRoot x EndRoot) minus 10 (RootIndex 4 StartRoot 2 y EndRoot)
35 (RootIndex 4 StartRoot x EndRoot) minus 18 (RootIndex 4 StartRoot 2 y EndRoot)

All Answers 1

Answered by GPT-5 mini AI
Rewrite each fourth root using factors: ∜(16x)=2∜x, ∜(81x)=3∜x, ∜(2y)=∜2·∜y, ∜(32y)=2∜2·∜y. Then

2·∜(16x)+3·∜(81x)=2·(2∜x)+3·(3∜x)=4∜x+9∜x=13∜x,

and

-2·∜(2y)-4·∜(32y)=-2∜2∜y-4·(2∜2∜y)=(-2-8)∜2∜y=-10∜(2y).

So the simplified form is 13∜x - 10∜(2y).