Answer:
Step-by-step explanation:
12a)To rationalize the denominator, multiply the denominator and numerator by √5.
[tex]\frac{15}{\sqrt{5}}=\frac{15*\sqrt{5}}{\sqrt{5}*\sqrt{5}}\\\\=\frac{15\sqrt{5}}{5}\\\\=3\sqrt{5}[/tex]
b) (a+b)² = a² + 2ab + b²
(1 +√3)² = 1² + 2*1*√3 + (√3)²
= 1 + 2√3 + 3
= 4 + 2√3
a = 4 ; b =2
13) (a + b)(a - b) = a² - b²
[tex]\frac{(6-\sqrt{5})(6+\sqrt{5})}{\sqrt{31}}=\frac{6^{2}-(\sqrt{5})^{2}}{\sqrt{31}}\\\\ =\frac{36-5}{\sqrt{31}}\\\\=\frac{31}{\sqrt{31}}\\\\=\frac{31*\sqrt{31}}{\sqrt{31}*\sqrt{31}}\\\\=\frac{31\sqrt{31}}{31}\\\\=\sqrt{31}[/tex]
