Question

Pls help rationalize

Answer 1

Answer:

See answers below.

Step-by-step explanation:

All of these use the same idea: multiply numerator and denominator by the conjugate radical (an identical expression but with the sign between terms changed).

$\frac{1}{13-\sqrt{15}}\cdot\frac{13+\sqrt{15}}{13+\sqrt{15}}=\frac{13+\sqrt{15}}{169-15}}\\\\=\frac{13+\sqrt{15}}{154}$

$\frac{1}{\sqrt{13}-\sqrt{11}} \cdot \frac{\sqrt{13}+\sqrt{11}}{\sqrt{13}+\sqrt{11}}=\frac{\sqrt{13}+\sqrt{11}}{13-11}\\\\=\frac{\sqrt{13}+\sqrt{11}}{2}$

$\frac{1}{\sqrt{21}+\sqrt{29}}\cdot\frac{\sqrt{21}+\sqrt{29}}{\sqrt{21}+\sqrt{29}}=\frac{\sqrt{21}+\sqrt{29}}{21-29}\\\\=\frac{\sqrt{21}+\sqrt{29}}{-8}$

Note:  Here's an example of what happens when you multiply conjugate radicals.

$(\sqrt{13}-\sqrt{11}})(\sqrt{13}+\sqrt{11})=13-\sqrt{11}\sqrt{13}+\sqrt{13}\sqrt{11}-11=13-11$

When you FOIL those binomials, the square roots go away!

Answer 2

Answer:

1=  0.109

2= 3.46

3 = -(minus)1.24

Step-by-step explanation: