Answer:
Step-by-step explanation:
6)a)
[tex]5\sqrt{27}=5\sqrt{3*3*3}\\\\ =5*3\sqrt{3}\\\\ =15\sqrt{3}[/tex]
7a) y² - 5y - 14 = y² -7y +2y - 2*7
= y*(y - 7) + 2*(y - 7)
=(y - 7)(y + 2)
b) Use FOIL method
[tex](2\sqrt{5}+1)(3\sqrt{5}-1)=(2\sqrt{5}*3\sqrt{5})-((2\sqrt{5}*1)+1*3\sqrt{5})-1*1\\\\ =6*5-2\sqrt{5}+3\sqrt{5}-1\\\\ =30+(-2+3)\sqrt{5}-1\\ \\=29+\sqrt{5}[/tex]
c) Rationalize the denominator by multiplying the denominator and numerator by √12
[tex]\frac{6}{\sqrt{12}}=\frac{6*\sqrt{12}}{\sqrt{12}*\sqrt{12}}\\\\=\frac{6\sqrt{2*2*3}}{12}\\\\=\frac{6*2\sqrt{3}}{12}\\\\=\frac{12\sqrt{3}}{12}\\\\=\sqrt{3}[/tex]
