HardMathematicsHigh School (9–10)GeneralNumber Systems › Exponents and RadicalsNumerical

Find the rational numbers a and b if (√6 - 2)/(√6 + 2) = a - b√6.

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Find the rational numbers $a$ and $b$ if $\dfrac{\sqrt{6} - 2}{\sqrt{6} + 2} = a - b\sqrt{6}$ .

Need a reminder? The key ideaShow

To clear a root from the bottom, multiply the top and the bottom by the same number: by $\sqrt{a}$ for $\dfrac{1}{\sqrt{a}}$ , and by the conjugate $a - \sqrt{b}$ for $\dfrac{1}{a + \sqrt{b}}$ . The value does not change.

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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