Simplify square root of (32a^4)/(b^2)

Problem

√(,(32*a4)/(b2))

Solution

1. Apply the quotient rule for radicals to separate the numerator and the denominator.

√(,32*a4)/√(,b2)

2. Factor the radicand in the numerator to identify perfect squares.

√(,16⋅2⋅(a2)2)/√(,b2)

3. Simplify the numerator by taking the square root of 16 and (a2)2

(4*a2√(,2))/√(,b2)

4. Simplify the denominator by taking the square root of b2

(4*a2√(,2))/|b|

Final Answer

√(,(32*a4)/(b2))=(4*a2√(,2))/|b|

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