Evaluating radical expression means, we have apply the value instead of the variable that we find in the square root.If it is possible we can simplify the radical.

Let us see some example problems to understand this concept more clearly.

Example 1 :

Use the following function rule to find f(169).

(x) = √(185 - x)

Solution :

To find the value of f(169) first we have to apply 169 instead of x in the given function f(x).

(x) = 2 √(185 - x)

(169) = 2 √(185 - 169)

=  2√16

=  2√(4 x 4)

=  2(4) ==> 8

Hence the value of f (169) is 8.

Example 2 :

Use the following function rule to find f(3).

(x) = 5√x³

Solution :

To find the value of f(3) first we have to apply 3 instead of x in the given function f(x).

(x) =  5√x³

(3) =  5 √3³

=  5 √(3 x 3 x 3)

=   5 x 3 √3  ==>  15√3

Hence the value of f (3) is 15√3.

Example 3 :

Use the following function rule to find f(1).

f(x) = 5 x + 1

Solution :

To find the value of f(1) first we have to apply 1 instead of x in the given function f(x).

f(x) = 5 x + 1

f(1) = 5 √1 + 1

= 5 (1) + 1

= 5 + 1 ==> 6

Hence the value of f(1) is 6.

Example 4 :

Use the following function rule to find f(25).

f(x) = √(x/49)

Solution :

To find the value of f(25) first we have to apply 25 instead of x in the given function f(x).

f(x) = √(x/49)

f(25) = √(25/49)

= √(5 x 5)/(7 x 7)

= 5/7

Hence the value of f(25) is 5/7.

Example 5 :

Evaluate the following radical function if x = 3 and y = 4

f(x) = √(x² + y²)

Solution :

f(x) = √(x² + y²)

Now we have to apply the values 3 and 4 instead of x and y respectively.

f(x) =  √(3² + 4²)

=  √(9 + 16) ==> √25

=  √(5x 5) = 5

Hence the simplified value 5.

After having gone through the stuff given above, we hope that the students would have understood "Evaluate radical expressions".

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