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9.3: Властивості поділу радикалів
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\(\sqrt{\frac{2}{1485}} = \sqrt{\frac{2}{3^3 \cdot 5 \cdot 11}} = \sqrt{\frac{2}{3^3 \cdot 5 \cdot 11} \cdot \frac{3 \cdot 5 \cdot 11}{3 \cdot 5 \cdot 11}} = \sqrt{\frac{2 \cdot 3 \cdot 5 \cdot 11}{3^... $\sqrt{\frac{2}{1485}} = \sqrt{\frac{2}{3^3 \cdot 5 \cdot 11}} = \sqrt{\frac{2}{3^3 \cdot 5 \cdot 11} \cdot \frac{3 \cdot 5 \cdot 11}{3 \cdot 5 \cdot 11}} = \sqrt{\frac{2 \cdot 3 \cdot 5 \cdot 11}{3^4 \cdot 5^2 \cdot 11^2}} = \frac{\sqrt{2 \cdot 3 \cdot 5 \cdot 11}}{3^2 \cdot 5 \cdot 11} = \frac{\sqrt{330}}{494}$
8.2: Спрощення радикальних виразів
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\[\begin{array}{rlrl}{a^{2}+b^{2}} & {=c^{2}} & {} & \color {Red} {\text { Pythagorean Theorem. }} \\ {x^{2}+x^{2}} & {=8^{2}} & {} & \color {Red} {\text { Substitute: } x \text { for } a, x \text { f... $\begin{array}{rlrl}{a^{2}+b^{2}} & {=c^{2}} & {} & \color {Red} {\text { Pythagorean Theorem. }} \\ {x^{2}+x^{2}} & {=8^{2}} & {} & \color {Red} {\text { Substitute: } x \text { for } a, x \text { for } b, 8 \text { for } c .} \\ {2 x^{2}} & {=64} & {} & \color {Red} {\text { Combine like terms: } x+x=2 x} \\ {x^{2}} & {=32} & {} & \color {Red} {\text { Divide both sides by } 2}\end{array} \nonumber$