Question

How do you simplify `sqrt(5) - sqrt(2)`?

Answer 1

See below.

Explanation:

When combining radicals, it is important to remember that you can only combine them through multiplication and division.

Otherwise, to solve something like this, you find the values for each radical and solve from there.

The best way to explain this, is instead of just thinking of them as radicals, think of them as having exponents .

The exponent to represent the `sqrt` of a number is `1/2`, where the denominator is the index of the radical, and the numerator is the power in which the number inside is being effected.

So now we can see this expression as:

`sqrt(5)-sqrt2 => 5^(1/2) - 2^(1/2)`

Seeing this, we can tell that the two terms do not combine, because the base numbers are different. Therefore, this expression is already simplified.

Now if we wanted to solve the expression, instead of simplifying, we simply find each value and solve:

`sqrt(5)-sqrt2`

`=2.236-1.414`

`=0.822`