SOLVING EQUATIONS WITH RADICALS ON BOTH SIDES

The following steps will be useful to solve equations with radicals on both sides.

Step 1 :

Square both sides to get rid of the radicals.

Step 2 :

Simplify and solve for the variable.

Example 1 :

Solve for x :

√x  =  5√2

Solution :

√x  =  5√2

Square both sides. 

(√x)²  =  (5√2)²

x  =  5²(√2)²

x  =  25(2)

x  =  50

Example 2 :

Solve for y :

√-y  =  3√7

Solution :

√-y  =  3√7

Square both sides. 

(√-y)²  =  (3√7)²

-y  =  3²(√7)²

-y  =  9(7)

-y  =  63

Multiply each side by -1. 

y  =  -63

Example 3 :

Solve for x : 

√(3x + 12)  =  3√3

Solution :

√(3x + 12)  =  3√3

Square both sides. 

[√(3x + 12)]²  = (3√3)²

3x + 12  =  3²(√3)²

3x + 12  =  9(3)

3x + 12  =  27

Subtract 12 from each side.

3x  =  15

Divide each side by 3.

x  =  5

Example 4 :

Solve for x : 

√(x - 5)  =  2√6

Solution :

√(x - 5)  =  2√6

Square both sides. 

[√(x - 5)]²  = (2√6)²

x - 5  =  2²(√6)²

x - 5  =  4(6)

x - 5  =  24

Add 5 to each side. 

x  =  29

Example 5 :

Solve for x : 

√(3x - 4)  =  √6

Solution :

√(3x - 4)  =  √6

Square both sides.

[√(3x - 4)]²  =  (√6)²

3x - 4  =  6

Add 4 to each side. 

3x  =  10

Divide each side by 3

x  =  10/3

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