1 Answer

Emmanuel Rodriguez · Answer 1 · 2024-06-21T08:40:04+0000

The simplified form of the radical expressions are now listed below:

Case 3:
(10 - 2√(3))/(11)}

Case 4:
(6+√(4))/(32)

How to simplify radical expressions by rationalization

In this questions we find two cases of radical expressions of the form:

$(a)/(b \pm √(c))$ , where a, b, c are real constants.

Whose solution is introduced and explained below:

$(a)/(b\pm √(c))\cdot (b \mp √(c))/(b \mp √(c))$

$(a\cdot (b \mp √(c)))/(b^2 - c)$

This procedure is known as rationalization, that is, eliminating the radical elements of denominator. This is an application of algebra properties.

Now we proceed to determine the simplified form of each radical expression by rationalization, that is, eliminating radical terms on denominator:

Case 3:

(4)/(5+√(3))

$(4\cdot (5 - √(3)))/((5 + √(3))\cdot (5 - √(3)))$

(20-4√(3))/(25 - 3)

(20 - 4√(3))/(22)

(10 - 2√(3))/(11)}

Case 4:

(1)/(6 - √(4))

$((6 + √(4)))/((6 - √(4))\cdot (6 + √(4)))$

(6 + √(4))/(36 - 4)

(6+√(4))/(32)

The solutions to radical expression are: Case 3:
(10 - 2√(3))/(11)} , Case 4:
(6+√(4))/(32) .

Please log in or register to add a comment.