Question

4√2 + 5√2 by √48 +√ 18

Answer 1

Required to find

(4√2 + 5√2 ) / (√48 + √18)

[√48 = √(6×8) = √(2×3×2×4) = √(3 ×(2×2×4)) =
√(3 ×(16)) = √3 × √16 = √3 × 4 = 4√3]

[√18 = √(2×9) = √2 × √9 = √2 × 3 = 3√2]

So we can write it as..

4√2 + 5√2 / 4√3 + 3√2

multiply and Divide it with (4√3 - 3√2)

(4√2 + 5√2)(4√3 - 3√2) / (4√3 + 3√2)(4√3 - 3√2)

[4√2(4√3) + 5√2(4√3) - 4√2(3√2) - 5√2(3√2)]/ [ (4√3)^2 - (3√2)^2]

[16√6 + 20√6 - 12(2) - 15(2) ] / [ 16(3) - 9(2)]

[36√6 - 24 - 30] / [ 48 - 18]

[36√6 - 54] / [30]

cancellation of '2'

[18√6 - 27] / [15]

cancellation of '3'

[6√6 - 9] / [5] ...is the answer....