Disclaimer, not a native Russian speaker (and I think you have a typo and meant знаешь).
Well spotted! You're right (I think) the root of both words is зна which (according to Roots of the Russian Language) is "to know"
Beware, though. While knowing the roots and seeing the similarities can be helpful (at least to me), sometimes using that approach can make things very confusing. (The prefixes and suffixes can result in a meaning drastically different from the root. Sometimes it's very much a case of "you can't get there from here" with them)
But I've personally found it's useful to at least be aware of the roots and patterns even knowing that they can still lead me astray.
Значить is the infinitive. The stress is on the а.
The full conjugation in the present tense is:
Note, the stress in each of these conjugations is in on the а. (On the они значат conjugation, the stress is on the first а.)
In English, I use "to mean" in a couple different ways.
The first is "to signify" - as in, "My alarm ringing signifies (means) that I need to go to work."
The second is, "to intend to state" - as in, "By saying she likes me, she intends to state (means) that I am her friend."
Can значить (which means, "to mean, to signify") also be used in the second way of intention to state something, or is this better represented by another verb?
One of the ways to say it is to use the 'иметь в виду' or the 'под ... подразумевать' constructions. 'Говоря, что я ей нравлюсь, она имеет в виду, что я ее друг'. 'I need a volunteer. And by volunteer I mean you Jones' 'Мне нужен доброволец. И под добровольцем я подразумеваю тебя, Джонс' Though this construction is purely informative, it's used for explanation, not for emphasizing. Thus, 'I relly mean it!' cannot be translated using this construction. In this case I would use something like 'Я серьезно!'
Значит is being pronounced more like it's spelled значет, but that's the way it's pronounced - the и in значит sounds nothing like the single и = "and".
See: https://forvo.com/word/%D0%B7%D0%BD%D0%B0%D1%87%D0%B8%D1%82/#ru to hear native speakers pronounce is the same as the computer voice.