Question

Adding and subtraction radicals
2√7+5√3+4√7

Answer 1

To add or subtract radicals, you can combine like terms. In this case, you have the terms \(2\sqrt{7}\) and \(4\sqrt{7}\), which are like terms because they both contain \(\sqrt{7}\).

Let's combine the coefficients of \(\sqrt{7}\):

\[
2\sqrt{7} + 4\sqrt{7} = (2 + 4)\sqrt{7} = 6\sqrt{7}
\]

Now, you also have the term \(5\sqrt{3}\) which cannot be combined with any other terms, as it contains \(\sqrt{3}\).

So, putting it all together, the expression \(2\sqrt{7} + 5\sqrt{3} + 4\sqrt{7}\) simplifies to:

\[
6\sqrt{7} + 5\sqrt{3}
\]

This is the final simplified expression.