Question

How do you do this?

Answer 1

And these too

Answer 2

1. Use the fact that \(\sqrt{a^2} = a\) assuming \(a\) is positive and simplify each radical using the properties of radicals (which are mostly the same as exponents) and then add up like-terms.
\(\sqrt{ab} = \sqrt{a} \sqrt{b}\)

Answer 3

2. Distribute the \(\sqrt{t}\) into the binomial. Just make sure you simplify any perfect squares under radicals.
3. Same case as above, only with \(\sqrt{6}\).

Answer 4

4. Rationalize the denominator: multiply by the expression that will allow you to simplify the denominator to both numerator and denominator.
\[\begin{align} \quad \frac{a}{\sqrt{b}} &= \frac{a}{\sqrt{b}} \times \frac{\sqrt{b}}{\sqrt{b}} \\
&= \frac{a\sqrt{b}}{b} \end{align} \]