Radical Notation

An expression to have a square root called radicals. And it also has the square root. Radicals are called the exponent with limited power. Or else it can be defined as inverse power. We have different methods in radical notation. Here we are going to learn about radical notation.

Topics of radical notation:

Radical equations.

Radical inequalities.

Radical notation exponents.

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Solving radical equations:

Where the variables appear in the radicand, are called radical equations. The solution to these equations is based on this fact. If two real numbers are equal, And their squares are also equal.

Example 1:

(√(3x2 +10x) = 5.


Step 1:  Take square on both side

(√(3x2 +10x))2 = (5)2


Step 2: square root of (3x2 +10x) = (3x2 +10x)

Step 3: After simplification we get   (5)2  =  25

Step 4: 3x2 +10x = 25.

Step 5: It can be written as  3x2 +10x - 25 = 0

Step 6: Here we need to use the quadratic formula for finding x value ,

Step 7 :The formula   is (-b +- sqrt(b^2 -4ac))/(2a)

Step 8: 3x2 +10x - 25 = ((-10)  ± √(102 - (4 × 3 × (-25)))) / (2 × 3).

=  (-10 +- sqrt(100+300))/(6)

= (-10 +- sqrt(400))/(6)

= (-10 +- 20)/(6)

x    =    (-10 +20)/(6)        or   x = (-10-20)/6 (-10-20)/(6)

=  (10)/(6)            or      =  (-30)/(6)

Step 9: So the value of x = (5)/(3)            or        = -5

Example of Radical inequalities:

Radical inequalities are related to solving rational equations. But we have one more step to convert the radical number as a real number.

Example problem:

x+2  ≥ -3.

Solution:

Step 1: Square on both the sides, so(x+2 ) 2≥ (-3)2

Step 2: So now we have x+2 ≥ 9.

Step 3: Subtract using 2 on both the sides. Therefore x+2-2 >= 9-2.

Step 4:Therefore the answer is x >= 7.

Algebra is widely used in day to day activities watch out for my forthcoming posts on Greatest Integer Function and Chain Rule Differentiation. I am sure they will be helpful.

Radical exponents:

Simplify  (x^8 y^-3)/(x^-3 y^8)

Solution:

Step 1:  (x^8 y^-3)/(x^-3 y^8)

Step 2:    (x^8 x^3)/(y^8 y^3)

Step 3: After simplification (x^11)/(y^11)

Step 4: So the answer (x8 y-3 )/(x-3 y8 ) = (x/y)11