If x = √2 – 1, then write the value of \(\frac{1}{x}\).

1.	If x = √2 – 1, then write the value of \(\frac{1}{x}\).
Answer» \(x = \sqrt2-1\) \(\frac{1}{x} = \frac{1}{(\sqrt2-1)}\) Rationalising denominator, we have \(= \frac{1}{(\sqrt2-1)} \) x \(\frac {(\sqrt2+1)}{(\sqrt2+1)}\) \(= \frac{(\sqrt2+1)}{(2-1)}\) \(= \sqrt2+1\)

Answer»

\(x = \sqrt2-1\)

\(\frac{1}{x} = \frac{1}{(\sqrt2-1)}\)

Rationalising denominator, we have

\(= \frac{1}{(\sqrt2-1)} \) x \(\frac {(\sqrt2+1)}{(\sqrt2+1)}\)

\(= \frac{(\sqrt2+1)}{(2-1)}\)

\(= \sqrt2+1\)

Discussion

The simplest rationalising factor of 2√5 - √3 isA. 2√5 + 3B. 2√5 + C. √5 + √3D. √5 - √3
The simplest rationalising factor of √3+ √5 isA. √3 - 5B. 3 - √5C. √3 - √5D. √3 + √5
Simplify:(√8 – √2) (√8 + √2)
Simplify each of the following:(i) \(\sqrt[3]{4}\) x \(\sqrt[3]{16}\)(ii) \(\frac{\sqrt[4]{1250}}{\sqrt[4]{2}}\)
Simplify:(3 + √3)(5 - √2)
Simplify:(3 + √3) (3 – √3)
Simplify:(4 + √7) (3 + √2)
Simplify:(√5 – √2) (√5 + √2)
Simplify:(√3 + √7)2
Simplify:(√5 – √3)2.