Question

Evaluate: (4sqrt(3) - sqrt(2))(3sqrt(2) + 2sqrt(3))​

Answer 1

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(4√3 - √2)(3√2 + 2√3)

(2(√2)²√3 - √2)((√3)²√2 + 2√3)

{√2[2√2√3 - 1]}{√3(√3√2 + 2)}

{√2[2√6 - 1]}{√3(√6 + 2)}

√6(2√6 - 1)(√6 + 2)

√6(2(6) + 4√6 - √6 - 2)

√6 ( 12 - 2 + 3√6)

√6(10 + 3√6)

10√6 + 3(6)

10√6 + 18

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Answer 2

Answer:

The simplification of given number is

$(4\sqrt{3} -\sqrt{2}) ({3\sqrt{2} +2\sqrt{3} } )=10\sqrt{6} +18$

Step- by- step explanation:

The given product of irrational numbers is

$(4\sqrt{3} -\sqrt{2}) ({3\sqrt{2} +2\sqrt{3} } )$

From the above number we observe that both the numerator and the denominator are having irrational terms.Hence, to simplify the below number we shall explain it by multiplying and dividing the number with a attributing factor.We first explain the denominator in the following way-

$(4\sqrt{3} -\sqrt{2}) ({3\sqrt{2} +2\sqrt{3} } )=12\sqrt{6} +24-6-2\sqrt{6} \\=10\sqrt{6} +18$

We observe that the denominator of the number is successfully accounted and if we further continue vindication grounded on numerator, we will again get irrational terms in the denominator.Hence, we stop it by here.Therefore, the final answer is

$(4\sqrt{3} -\sqrt{2}) ({3\sqrt{2} +2\sqrt{3} } )=10\sqrt{6} +18$

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