1) (2-√3)² = 4 - 4√3 + 3 = 7 - 4√32√12 = 2√(43) = 22√3 = 4√3
Adding them together: 7 - 4√3 + 4√3 = 7
2) √50 = √(252) = 5√2√32 = √(162) = 4√21/3 √18 = √(9*2)/3 = 3√2/3 = √2
Subtracting and simplifying: 5√2 - 4√2 - √2 = 0
3) 6√2 - √2 (√2 + √36) = 6√2 - √2 (√2 + 6) = 6√2 - √(22 + 2*6) = 6√2 - √(4 + 12) = 6√2 - √16 = 6√2 - 4√2 = 2√2
1) (2-√3)² = 4 - 4√3 + 3 = 7 - 4√3
2√12 = 2√(43) = 22√3 = 4√3
Adding them together: 7 - 4√3 + 4√3 = 7
2) √50 = √(252) = 5√2
√32 = √(162) = 4√2
1/3 √18 = √(9*2)/3 = 3√2/3 = √2
Subtracting and simplifying: 5√2 - 4√2 - √2 = 0
3) 6√2 - √2 (√2 + √36) = 6√2 - √2 (√2 + 6) = 6√2 - √(22 + 2*6) = 6√2 - √(4 + 12) = 6√2 - √16 = 6√2 - 4√2 = 2√2