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

ab=ab
To remove the radical on the left side of the equation, square both sides of the equation.
ab2=(ab)2
Simplify each side of the equation.
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
Solve for a.
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

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