Simplify

Problem

4*a*b√(,2*b)−3*a√(,18*b3)+7*a*b√(,6*b)

Solution

1. Identify the terms in the expression that can be simplified, specifically the middle term containing the square root of a power and a composite number.

2. Factor the radicand in the second term to pull out perfect squares.

18*b3=9⋅2⋅b2⋅b

3. Simplify the square root of the second term by taking the square root of the perfect squares 9 and b2

√(,18*b3)=3*b√(,2*b)

4. Substitute this simplified radical back into the second term of the original expression.

3*a*(3*b√(,2*b))=9*a*b√(,2*b)

5. Rewrite the entire expression with the simplified second term.

4*a*b√(,2*b)−9*a*b√(,2*b)+7*a*b√(,6*b)

6. Combine the like terms that contain the same radical factor √(,2*b)

(4*a*b−9*a*b)√(,2*b)=−5*a*b√(,2*b)

7. Combine the result with the remaining term to reach the final simplified form.

−5*a*b√(,2*b)+7*a*b√(,6*b)

Final Answer

4*a*b√(,2*b)−3*a√(,18*b3)+7*a*b√(,6*b)=−5*a*b√(,2*b)+7*a*b√(,6*b)

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