Question

How do you simplify `sqrt21+sqrt35`#?

Answer 1

All radicals are now simplified and both radicands no longer have any square factors.

Explanation:

Every non-negative real number a has a non-negative square root called the principal square root, which is denoted by `√a`, where `√` is called the radical sign.

For example,
The principal square root of `9` is `3`, denoted `√9 =3`

The term whose root is being considered is known as the radicand. The radicand is the number or expression underneath the radical sign, in the example above, `9`.

And so, to simplify a square root, we extract factors which are squares, for example, factors that are raised to an even exponent, like the examples shown above.

In this case, however, all the factors are only raised to the first power and this means that both of the square roots cannot be simplified.

You could change the surds to a form such as

`sqrt(3)sqrt(7)+sqrt(5)sqrt(7)`

But this is not simplifying them