Question

Evaluate: (4√ (3) - √ (2))(3√ (2) + 2√ (3))

Answer 1

To evaluate (4√(3) - √(2))(3√(2) + 2√(3)), we can use the FOIL method. Multiplying the binomials gives us 10√(6) + 18.

Step-by-step explanation:

We can evaluate the expression using the FOIL method. FOIL stands for First, Outer, Inner, Last, and it is used to multiply two binomials. In this case, we have two binomials: (4√(3) - √(2)) and (3√(2) + 2√(3)).

1. Multiply the First terms: (4√(3)) * (3√(2)) = 12√(6)
2. Multiply the Outer terms: (4√(3)) * (2√(3)) = 8√(9)
3. Multiply the Inner terms: (-√(2)) * (3√(2)) = -3√(4)
4. Multiply the Last terms: (-√(2)) * (2√(3)) = -2√(6)

Combine the like terms: 12√(6) + 8√(9) - 3√(4) - 2√(6).

Simplify further: 12√(6) - 2√(6) + 8√(9) - 3√(4).

Combine the like terms again: 10√(6) + 8√(9) - 3√(4).

Finally, simplify the radicals if possible: 10√(6) + 8√(9) - 3√(4) = 10√(6) + 8(3) - 3(2) = 10√(6) + 24 - 6 = 10√(6) + 18.

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