ab=ab

To remove the radical on the left side of the equation, square both sides of the equation.

ab2=(ab)2

Multiply the exponents in ((ab)12)2.

Apply the power rule and multiply exponents, (am)n=amn.

(ab)12⋅2=(ab)2

Cancel the common factor of 2.

Cancel the common factor.

(ab)12⋅2=(ab)2

Rewrite the expression.

(ab)1=(ab)2

(ab)1=(ab)2

(ab)1=(ab)2

Simplify.

ab=(ab)2

Combine using the product rule for radicals.

ab=ab2

Rewrite ab2 as ab.

Use axn=axn to rewrite ab as (ab)12.

ab=((ab)12)2

Apply the power rule and multiply exponents, (am)n=amn.

ab=(ab)12⋅2

Combine 12 and 2.

ab=(ab)22

Cancel the common factor of 2.

Cancel the common factor.

ab=(ab)22

Divide 1 by 1.

ab=(ab)1

ab=(ab)1

Simplify.

ab=ab

ab=ab

ab=ab

Move all terms containing a to the left side of the equation.

Subtract ab from both sides of the equation.

ab-ab=0

Subtract ab from ab.

0=0

0=0

Since 0=0, the equation will always be true.

Always true

Always true

The result can be shown in multiple forms.

Always true

Interval Notation:

(-∞,∞)

Solve for a square root of ab = square root of a square root of b