Radicals are simply numbers under the power root such as the square root. For example, (√̅2). But √̅4 is not a radical as being equal to 2, so it’s just an integer.
The simple point (and typical way) to introduce square root is to find the side of a square when the area A is given. The side must be √̅A — it’s just an integer! Or we can introduce radicals when studying Pythagorean Theorem for the right triangles. If wo straight edges of the triangle are a respectively b, and the hypotenuse c, then a2 + b2 = c2, or c = square-root of (a2 + b2). Number c is a radical if a2 + b2 is NOT a perfect square.
We have collected a few articles related to the radicals /square roots. Take a look as you like.
(i) Irrational Roots. You’re used to working with quadratics with integer roots, but what about when the roots are irrational?
(ii) Staircase Sequences. Can you make sense of these unusual fraction sequences?
(iii) Nested Surds.
For a quick peep, (i) discusses the irrational roots resulted from solving a quadratic equation, esp. conjugate roots when coefficients of the equation are all integers; In (ii) we consider a staircase sequence, each one is a usual fraction (like 1/2 oe 2/3), but the sequence leads to irrationals; and in (c) we eventually go into double radicals: that is, we have square root under the square root, like square-root of (2+√̅3): for some of them, it is possible to simplify so as to use ONLY ONE layer of square-root!
All those are fun and thought-provoking!