Question

show me a square root simble

Answer 1

Simplify. Rationalize the denominator

-square root7 / 3 + square root 3

Answer 2

The square root symbol is represented as \( \sqrt{} \). For example, the square root of 16 is written as \( \sqrt{16} \), which equals 4.

Answer 3

To simplify and rationalize the denominator of the expression \(\frac{\sqrt{7}}{3 + \sqrt{3}}\), we can multiply the numerator and denominator by the conjugate of the denominator, which is \(3 - \sqrt{3}\).

Here are the steps:

1. **Multiply by the conjugate:**

\[
\frac{\sqrt{7}}{3 + \sqrt{3}} \cdot \frac{3 - \sqrt{3}}{3 - \sqrt{3}} = \frac{\sqrt{7}(3 - \sqrt{3})}{(3 + \sqrt{3})(3 - \sqrt{3})}
\]

2. **Simplify the denominator:**

The denominator is a difference of squares:

\[
(3 + \sqrt{3})(3 - \sqrt{3}) = 3^2 - (\sqrt{3})^2 = 9 - 3 = 6
\]

3. **Expand the numerator:**

\[
\sqrt{7}(3 - \sqrt{3}) = 3\sqrt{7} - \sqrt{21}
\]

4. **Combine the results:**

Now we have:

\[
\frac{3\sqrt{7} - \sqrt{21}}{6}
\]

5. **Final simplification:**

We can separate the terms in the fraction:

\[
\frac{3\sqrt{7}}{6} - \frac{\sqrt{21}}{6} = \frac{\sqrt{7}}{2} - \frac{\sqrt{21}}{6}
\]

Thus, the final simplified and rationalized expression is:

\[
\frac{\sqrt{7}}{2} - \frac{\sqrt{21}}{6}
\]