Question

Simplify (7sqrt3 - 4sqrt6 + sqrt48 - sqrt54)

1) 11sqrt{6} - 7sqrt{12}
2) 11sqrt{3} - 7sqrt{6}
3) -3sqrt{9}
4) 4sqrt{9}

Answer 1

To simplify the given expression, one must break down the square roots of 48 and 54 into their prime factors, combine like terms, and simplify. The result is the expression 11√3 - 7√6.

Step-by-step explanation:

To simplify the expression (7√3 - 4√6 + √48 - √54), we will simplify each square root separately and combine like terms. First, recognize that √48 and √54 can be simplified further:

√48 = √(16 × 3) = √16 × √3 = 4√3√54 = √(9 × 6) = √9 × √6 = 3√6

Now substitute these simplified forms back into the original expression:

(7√3 - 4√6 + 4√3 - 3√6)

Combine like terms:

(7√3 + 4√3) - (4√6 + 3√6)

11√3 - 7√6

This matches option 2, which is the simplified form of the given expression