Evaluate

Problem

(5√(,10)−2)*(4√(,6)+3)

Solution

1. Apply the FOIL method to multiply the two binomials by distributing each term in the first parentheses to each term in the second parentheses.

(5√(,10))*(4√(,6))+(5√(,10))*(3)+(−2)*(4√(,6))+(−2)*(3)

2. Multiply the coefficients and radicals in the first term using the property √(,a)⋅√(,b)=√(,a*b)

20√(,60)+15√(,10)−8√(,6)−6

3. Simplify the radical √(,60) by factoring out the largest perfect square, which is 4

√(,60)=√(,4⋅15)=2√(,15)

4. Substitute the simplified radical back into the expression and multiply by the coefficient.

20*(2√(,15))+15√(,10)−8√(,6)−6

5. Combine the terms to reach the final simplified form.

40√(,15)+15√(,10)−8√(,6)−6

Final Answer

(5√(,10)−2)*(4√(,6)+3)=40√(,15)+15√(,10)−8√(,6)−6

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