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38. Simplify: 3 √54


+2 √24

a) 13 √6

b) 5 √78

c) 35 √6

d) 30 √5

e) None of these

User Tomekwi
by
8.5k points

1 Answer

3 votes

Answer:

To simplify the given expression, we can first break down the numbers under the square roots into their prime factorization.

The prime factorization of 54 is 2 * 3^3, and the prime factorization of 24 is 2^3 * 3.

Using this, we can simplify the expression:

3√54 + 2√24 = 3√(2 * 3^3) + 2√(2^3 * 3)

= 3√(2 * 3 * 3 * 3) + 2√(2 * 2 * 2 * 3)

= 3√(2^1 * 3^2) * √3 + 2√(2^1 * 2^2) * √3

= 3 * 3√(2^1 * 3^2) + 2 * 2√(2^1 * 2^2) * √3

= 9√(2 * 3^2) + 4√(2^2 * 3)

= 9√(2 * 9) + 4√(4 * 3)

= 9√(2) * √9 + 4√(4) * √3

= 9√2 * 3 + 4√3 * 2

= 27√2 + 8√3

Therefore, the simplified expression is 27√2 + 8√3.

None of the answer choices given match this expression, so the correct option is e) None of these.

Explanation:

User Naphstor
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