Question

rationalise the denominator
$\sqrt{5 + \sqrt{2 \ \sqrt{5 - \sqrt{2} }$
​

Answer 1

Answer:

(√5 - √2 )/ (√5 + √2)

Multiply with the rational conjugate of the denominator.. in the numerator and denominator.

\begin{gathered}\frac{(\sqrt5-\sqrt2)*(\sqrt5-\sqrt2)}{(\sqrt5+\sqrt2)*(\sqrt5-\sqrt2)}\\\\=\frac{5+2-2\sqrt{10}}{5-2}\\\\=\frac{7}{3}-\frac{2}{3}\sqrt{10}\end{gathered}

(5 + 2)∗(5 − 2)

(5 − 2)∗(5 − 2)

=

5+2−2√10

5-2

= 7/3−2/3√10