You can combo this card with "Double or Nothing!" by using its effect on your own monster (assuming that monster is an Xyz Monster, otherwise Number 39: Utopia Roots won't gain any ATK).
Use cards that only work against non-Xyz Monsters like "Gravity Bind" and "Level Limit - Area B" to prevent this card from being destroyed by non-Xyz Monsters. However, a Burning Abyss deck can easily bypass this combo due to their monsters being level 3, so including "Weed Out" in your Side Deck is recommended.
Alternatively, you can use "Number Wall" and, to a lesser degree, "Number 66: Master Key Beetle", as both cards can protect "Utopia Roots" from being destroyed (using all three cards can create a three-card combo that protects each other from destruction, whether it be by battle or effects).
You can rapidly increase this card's ATK by summoning it in the same turn as another high-rank Xyz Monster you control. Attack with that other monster first and negate its attack. Then immediately attack with the now-buffed "Number 39: Utopia Roots".
In a Utopia deck, this card can be summoned along with Number 99: Utopic Dragon in a single turn. Using this method on Hope Dragun will give you a monster with 5500 Attack.
Since there are many easy ways to summon a Rank 8 monster, you can use this technique to turn "Number 39: Utopia Roots" into a 4500 ATK beat-stick. If you then manage to hold on to both monsters for another turn, that will turn into 8500 ATK (because the ATK gain is permanent).