Question

rationalise 1) 4 + 3 root 5 Upon 4 minus 3 root 5​

Answer 1

$\bf{\underline{Question:-}}$

• Rationalize 4 + 3√5/4-3√5

$\bf{\underline{Solution:-}}$

• On Rationalizing

$\bf\large:→ \frac{4+3\sqrt{5}}{4-3\sqrt{5}} × \frac{4+3\sqrt{5}}{4+3\sqrt{5}}$

• using ( a + b )² = a² +2ab +b² and
• a² + b² = (a + b ) ( a - b )

$\bf\large:→ \frac{4+3\sqrt{5} × 4+3\sqrt{5} }{4^2 - 3\sqrt{5}^2}$

$\bf:→ \large\frac{4^2 + 2×4×3\sqrt{5}+3\sqrt{5}^2}{16 - 15}$

$\bf :→\frac{16+24\sqrt{5}+45}{1}$

$\bf:→ 61+24\sqrt{5}$

$\bf{\underline{Hence:-}}$

• Rationalized.