Evaluate

Problem

2*(√(,216)+4√(,54))

Solution

1. Simplify the first radical by finding the largest perfect square factor of 216

216=36⋅6

√(,216)=√(,36⋅6)=6√(,6)

2. Simplify the second radical by finding the largest perfect square factor of 54

54=9⋅6

√(,54)=√(,9⋅6)=3√(,6)

3. Substitute the simplified radicals back into the expression.

2*(6√(,6)+4*(3√(,6)))

4. Multiply the coefficients inside the parentheses.

2*(6√(,6)+12√(,6))

5. Combine the like terms (the square roots of 6 inside the parentheses.

6√(,6)+12√(,6)=18√(,6)

6. Distribute the 2 outside the parentheses to find the final value.

2⋅18√(,6)=36√(,6)

Final Answer

2*(√(,216)+4√(,54))=36√(,6)

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