Make expressions equal to 6 using exactly four 4s

• You must use all four 4s.

• You may use addition (+).

• You may use subtraction (-).

• You may use multiplication, such as with asterisks (*) and/or grouping symbols.

• You may not use any division.

• You may not use decimal points.

• You may not use any concatenation.

• You may use grouping symbols, such as parentheses and/or brackets.

• You may not use any type of factorial signs.

• You may use up to four square root symbols, including the use of nested square roots.

• You may not use exponentiation.

• You may not use logarithms.

• You may not use trigonometric functions.

• You may not use any other numbers, characters, or operations, to include no other roots.

• This is in base 10.

Try to create and post 10 additional --> essentially <-- different solutions.

Permutations are the same.

This was moved to this site, because it is a math puzzle.

I think these are all essentially different and within the rules

1. $$\sqrt{4} + 4 + 4 - 4 = 6$$
2. $$\sqrt{4} + 4 + \sqrt{4} - \sqrt{4} = 6$$
3. $$\sqrt{\sqrt{4\times 4}} + \sqrt{4 \times 4} = 6$$
4. $$\sqrt{\sqrt{4\times 4}} +\sqrt{4} + \sqrt{4} = 6$$
5. $$(\sqrt{4} \times 4) - 4 + \sqrt{4} = 6$$
6. $$\sqrt{4 \times 4 \times 4} - \sqrt{4} = 6$$
7. $$\sqrt{4 \times 4} + 4 - \sqrt{4} = 6$$
8. $$((4-\sqrt{4}) \times 4) - \sqrt{4} = 6$$
9. $$\sqrt{\sqrt{4 \times 4} \times 4} + \sqrt{4} = 6$$
10. $$\sqrt{4+4-4} + 4 = 6$$

• I may post some additional solutions tomorrow. Jan 17 at 2:01

1. $$\ \sqrt{\sqrt{4\sqrt{4*4 \ } \ } \ } \ + \ 4 = \ 6$$
2. $$\ 4\sqrt{4} - \sqrt{\sqrt{4*4 \ } \ } = \ 6$$
3. $$\ 4 + 4 - \sqrt{\sqrt{4*4 \ } \ } = \ 6$$
4. $$\ \sqrt{(4 + \sqrt{4})(4 + \sqrt{4}) \ } = \ 6$$
5. $$\ \sqrt{ \sqrt{4 \ }(4*4 + \sqrt{4 \ }) \ } = \ 6$$
6. $$\ \sqrt{4*4\sqrt{4} + 4 \ } = \ 6$$
7. $$\ 4 + \sqrt{\sqrt{4 \ }(4 - \sqrt{4 \ }) \ } = \ 6$$