1) (√7-1)(√7+1) = (√7)^2 - 1^2 = 7 - 1 = 6
2) √75/√6 = √(25 3)/√6 = √25 √3 / √6 = 5√3 / √6 = 5√3 √6 / (√6 √6) = 5√18 / 6 = 5√3 √6 / 6 = 5√18 / 6 = (5√6 √3) / 6 = 5√18 / 6 = 5√6/2 = 5√6/2 = (5/2)√6
3) (3√2)^3 = 3^3 (√2)^3 = 27 √2^3 = 27 * 2 = 54
4) √64 - √12 + √75 = 8 - 2√3 + √(25 * 3) = 8 - 2√3 + 5√3 = 8 + 3√3
1) (√7-1)(√7+1) = (√7)^2 - 1^2 = 7 - 1 = 6
2) √75/√6 = √(25 3)/√6 = √25 √3 / √6 = 5√3 / √6 = 5√3 √6 / (√6 √6) = 5√18 / 6 = 5√3 √6 / 6 = 5√18 / 6 = (5√6 √3) / 6 = 5√18 / 6 = 5√6/2 = 5√6/2 = (5/2)√6
3) (3√2)^3 = 3^3 (√2)^3 = 27 √2^3 = 27 * 2 = 54
4) √64 - √12 + √75 = 8 - 2√3 + √(25 * 3) = 8 - 2√3 + 5√3 = 8 + 3√3