## Precalc week 4

This week in Precalc i was absent for the most part of the week so i only had two days of learning.   The most significant thing i learned was adding and subtracting radicals and defining variables.  Having the same radicand is only way to add and subtract radicals.  if the radicand is not the same then you must simplify the radical to find a common factor.

$2\sqrt{4x}$ $+4\sqrt{4x}=6 \sqrt{4x}$

x is greater than or equal to 0.

In lesson 2.4 we learned about dividing radicals.  You must rationalise the denominator by multiplying the top by the conjugate and then distribute and simplify.  Don’t forget to FOIL.

$5 \sqrt{5} - \sqrt{7 / }$ $5 \sqrt{3=}$ $3\sqrt{15} - \sqrt{21 / } 15$

In lesson 2.5 I learned about solving Radical equations.  I learned how to isolate a square root sign and determine the root of the equation and whether or not it’s a real root.  You can verify your answer by plugging x into the equation and checking to see if it matches.

$\sqrt{5x + 3} = \sqrt{3x +1}$

$2x = -2$

$x=-1$

It is not a real root