Question

in exercises 14–22, simplify the expression.

1. \\(\frac{3}{\sqrt{3}}\\) 15. \\(\frac{9}{\sqrt{5}}\\) 16. \\(\frac{\sqrt{3}}{\sqrt{50}}\\)
2. \\(\frac{4}{\sqrt{w}}\\) 18. \\(\frac{1}{\sqrt{5t}}\\) 19. \\(\sqrt{\frac{2z^2}{7}}\\)
3. \\(\frac{1}{\sqrt{6} - 1}\\) 21. \\(\frac{3}{4 + \sqrt{2}}\\) 22. \\(\frac{\sqrt{3}}{5 - \sqrt{}}
4. the average annual interest rate \\(r\\) (in decimal form) of a savings account

Explanation:

Step1: Simplify \(\frac{3}{\sqrt{3}}\)

Rationalize the denominator by multiplying numerator and denominator by \(\sqrt{3}\):
\(\frac{3\times\sqrt{3}}{\sqrt{3}\times\sqrt{3}}=\frac{3\sqrt{3}}{3}\)

Step2: Simplify the fraction

Cancel out the common factor 3:
\(\frac{3\sqrt{3}}{3}=\sqrt{3}\)

Answer:

\(\sqrt{3}\)