Wortelformules herleiden

(herleiden)
\(y = \sqrt{10 x} + \sqrt{27 x}\)
\(\text{} = \sqrt{10} ⋅ \sqrt{x} + \sqrt{27} ⋅ \sqrt{x}\)

(wortels berekenen)
\(y = 3{,}162... ⋅ \sqrt{x} + 5{,}196... ⋅ \sqrt{x}\)

\(y = -2{,}03 \sqrt{x}\)

(balansmethode)
\(7{,}3 \sqrt{{x \over 68}} = y\)
\(\sqrt{{x \over 68}} = {1 \over 7{,}3} ⋅ y\)
\(\sqrt{{x \over 68}} = 0{,}136... ⋅ y\)

(kwadrateren)
\({x \over 68} = (0{,}136... ⋅ y)^{2}\)
\({x \over 68} = (0{,}136...)^{2} ⋅ y^{2}\)

(balansmethode)
\(x = 68 ⋅ (0{,}136...)^{2} ⋅ y^{2}\)
\(x = 1{,}28 ⋅ y^{2}\)

(kruislings vermenigvuldigen)
\({y \over 1} = {x^{2} \over 812 ⋅ z}\)
\(x^{2} = y ⋅ 812 ⋅ z\)

(neem de wortel)
\(x = \sqrt{y ⋅ 812 ⋅ z}\)

(herleid)
\(x = \sqrt{812} ⋅ \sqrt{z ⋅ y}\)
\(x = 28{,}50 ⋅ \sqrt{z ⋅ y}\)