Card makers do not put in unnecessary components.
If the card would run properly on a single 8 pin connector, just one would have been included.
Yes, you need to connect both 6 and 8 pin.
On a similar vein, if your psu were capable of powering more than a single 8 pin connector, it would have it.
Lastly, 3000 series cards can have transient high power draws. You need more than average steady state capability.
What's the danger if you try?
If your card demands extra power, the connections are going to be over loaded and can damage the psu, motherboard or graphics card.
Your psu is a cheap unit, considered as tier 5 or 6 on this list:
Credit to @Starelementpokeand @Energycore for helping out with this long-awaited refresh of the old PSU tier list by Aniallation (who previously went several months without logging in), leaving the old list in need of help. This is simply an update of the list that was flawed in creation by the P...
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Time to replace the PSU.
Here is a handy chart for sizing:
http://www.realhardtechx.com/index_archivos/Page362.htm
I would buy at least 650w, preferably 750/850w.
You will find that a size up usually costs only a small increment.
The psu will only draw the power demanded of it, regardless of the max capability.
DO NOT buy a cheap psu.
A cheap PSU will be made of substandard components. It may not have all safety and overload protections.
The danger is if it fails under load, it can destroy anything it is connected to.
It will deliver advertised power only at room temperatures, not at higher temperatures found when installed in a case.
The wattage will be delivered on the 3 and 5v rails, not on the 12v rails where modern parts
like the CPU and Graphics cards need it. What power is delivered may fluctuate and cause instability
issues that are hard to diagnose.
The fan will need to spin up higher to cool it, making it noisy.
A cheap PSU can become very expensive.
Do not buy one.
A strong quality psu is a long term investment.
It will be good for many future upgrades.
One way to tell quality is to look at the warranty.
Look for a 7 to 10 year warranty.
Seasonic focus and Corsair rm units are a good place to start.
Yes. you will need to pay more.