Question

rationalise the denominator 1/√7-√6

Answer 1

★ √7+√6

★ refer to the attachment

Answer 2

Answer:

$\frac{1}{\sqrt{7}- \sqrt{6}}$= $(\sqrt{7}+\sqrt{6})$

Step-by-step explanation:

Given $\frac{1}{\sqrt{7}- \sqrt{6}}$

Multiply numerator and denominator by (√7+√6), we get

= $\frac{(\sqrt{7}+\sqrt{6})}</p><p>{(\sqrt{7}-\sqrt{6})(\sqrt{7}+\sqrt{6})}$

\* By algebraic identity:

(a+b)(a-b) = a²-b²

= $\frac{(\sqrt{7}+\sqrt{6})}{(\sqrt{7})^{2}-(\sqrt{6})^{2}}$

= $\frac{(\sqrt{7}+\sqrt{6})}{7-6}$

= $(\sqrt{7}+\sqrt{6})$

Therefore,

$\frac{1}{\sqrt{7}- \sqrt{6}}$= $(\sqrt{7}+\sqrt{6})$

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