Subtract. Simplify by collecting like radical terms, if possible.

To simplify , we first break down the square roots into simpler components. We know and .

Now we can substitute back into our expression:
or simply .

So,
.

It’s fascinating how mathematical concepts like simplifying radicals can be traced back to ancient civilizations. The Babylonians, around 2000 BC, were using methods that resembled our modern square root calculations. They had their ways of approximating square roots, and it shows that our quest for understanding numbers has a rich history!

In the real world, radicals often appear in various applications, especially when dealing with geometry. For instance, the Pythagorean theorem involves square roots when calculating the lengths of sides in right triangles, leading to more complex problems in physics or engineering where precise measurements are crucial. So understanding how to handle radicals can be quite beneficial!