MediumMathematicsHigh School (9–10)GeneralNumber Systems › Exponents and RadicalsNumericalBoard Exam SAT

Rationalise the denominator of 1/(√7 - √5).

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

Rationalise the denominator of $\dfrac{1}{\sqrt{7} - \sqrt{5}}$ . Check your answer with its value to three decimal places.

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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