Question

which uses associative property for equivalent expression of (i * rt7) * 5
i * (rt7 * 5)
35i
(rt7 * i) * 5
irt35
(rt means square root)

Answer 1

The associative property of multiplication is used when you regroup factors without changing their order: (ab)c = a(bc). So the expression that explicitly uses associativity is

- i * (rt7 * 5)

This is equivalent to the original (i * rt7) * 5. Also (rt7 * i) * 5 is equivalent too (it uses commutativity to swap i and rt7, then associativity to regroup).

The correct simplified form is 5·i·rt7 (usually written 5i√7). The other two given forms are incorrect:

- 35i is wrong because 5·√7 ≠ 35 (5·√7 ≈ 13.229, not 35).
- irt35 (i·√35) is wrong because √7·5 ≠ √35 (√7·5 = 5√7, while √35 = √7·√5).