Simplify

Problem

√(,7*x)*(√(,x)−7√(,7))

Solution

1. Distribute the term √(,7*x) to both terms inside the parentheses.

√(,7*x)⋅√(,x)−√(,7*x)⋅7√(,7)

2. Apply the product property of radicals, √(,a)⋅√(,b)=√(,a*b) to combine the terms.

√(,7*x^2)−7√(,49*x)

3. Simplify the radicals by identifying perfect squares within the radicands.

√(,x^2)⋅√(,7)−7⋅√(,49)⋅√(,x)

4. Evaluate the square roots of the perfect squares x^2 and 49

x√(,7)−7⋅7√(,x)

5. Multiply the constants in the second term to reach the final simplified form.

x√(,7)−49√(,x)

Final Answer

√(,7*x)*(√(,x)−7√(,7))=x√(,7)−49√(,x)

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