sqrt(s+2 sqrt(6))+sqrt(8-2 sqrt(15))

Question

Answer 1

To simplify the expression

, we need to find values of

that make the expression simpler.First, let's consider the term

. We can try to express it in the form

.Assume:

Squaring both sides:

By comparing rational and irrational parts, we get:

Solving these equations:

The solutions to these equations are the roots of the quadratic equation:

Solving this quadratic equation:

Thus,

and

. Therefore:

Now, consider the term

. We want to find

such that:

Squaring both sides:

By comparing rational and irrational parts, we get:

Solving these equations:

The solutions to these equations are the roots of the quadratic equation:

We need to find

such that the roots are real numbers. Let's assume

and

:

Thus:

Putting it all together:

Therefore, the simplified form of the given expression is:

Question