Question

Not a timed or graded assignment. Quick answer = amazing review :) please solve question 11 :)

Answer 1

we have the expression

`\frac{8}{3-\sqrt[]{10}}`

To simplify the given rational expression, multiply numerator and denominator by the conjugate of the denominator

so

`\frac{8}{3-\sqrt[]{10}}\cdot\frac{3+\sqrt[]{10}}{3+\sqrt[]{10}}`
`\frac{8}{3-\sqrt[]{10}}\cdot\frac{3+\sqrt[]{10}}{3+\sqrt[]{10}}=\frac{8\cdot(3+\sqrt[]{10})}{3^2-(\sqrt[]{10})^2}`
`\frac{8\cdot(3+\sqrt[]{10})}{3^2-(\sqrt[]{10})^2}=\frac{24+8\sqrt[]{10}}{9-10}`
`\frac{24+8\sqrt[]{10}}{-1}=-24-8\sqrt[]{10}`

therefore

The answer is

`-24-8\sqrt[]{10}`