Math pre cal 11
(11√3 - 3√12)＾2 without using calculator
11 √3 - 3 √3 √4
= 11 √3 - 3*2 √3
= 5√3
Still has to be squared
(5√3)^2
= 25*3
= 75
( 11 √3 - 3 √12 )² = [ 11 √3 - 3 ∙ √ (3 ∙ 4 ) ]² = ( 11 √3 - 3 ∙ √ 3 ∙ √ 4 )² =
( 11 √3 - 3 ∙ √ 3 ∙ 2 )² = ( 11 √3 - 6 √ 3 )² = ( 5 √ 3 )² = 5² ∙ √ 3² = 25 ∙ 3 = 75
Factor out sqrt 3:
(sqrt3*(11-6))^2,
(sqrt3*5)^2 = 75.
To simplify the expression (11√3 - 3√12)² without using a calculator, we need to follow a few steps:
Step 1: Expand the expression using the FOIL method.
(11√3 - 3√12)² = (11√3 - 3√12)(11√3 - 3√12)
Step 2: Apply the distributive property to each term in the first parentheses.
(11√3)(11√3) - (11√3)(3√12) - (3√12)(11√3) + (3√12)(3√12)
Step 3: Simplify each term.
121(√3)(√3) - 33(√3)(√12) - 33(√12)(√3) + 9(√12)(√12)
Step 4: Simplify the square roots.
121(3) - 33(√36) - 33(√36) + 9(√144)
Step 5: Evaluate the square roots.
363 - 33(6) - 33(6) + 9(12)
Step 6: Perform the multiplications.
363 - 198 - 198 + 108
Step 7: Combine like terms.
-33
Therefore, the simplified expression (11√3 - 3√12)² without using a calculator is -33.