Question

Simplify. 7 square root of 3 end root minus 4 square root of 6 end root plus square root of 48 end root minus square root of 54

A) 11 square root of 6 end root minus 7 square root of 12
B) 11 square root of 3 end root minus 7 square root of 6
C) negative 3 square root of 9
D) 4 square root of 9

Answer 1

The expression 7√3 - 4√6 + √48 - √54 simplifies to 11√3 - 7√6 after factoring and combining like terms, corresponding to option B.

Step-by-step explanation:

To simplify the given expression, we identify and combine like terms, specifically terms that involve the same radical component. Let's break it down step-by-step:

• The given expression is 7√3 - 4√6 + √48 - √54.
• We simplify √48 and √54 by factoring them into square roots of perfect squares and other integers: √48 = √(16×3) = 4√3 and √54 = √(9×6) = 3√6.
• Substitute the simplified terms back into the 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 gives us the final simplified form of the original expression: 11√3 - 7√6, which corresponds to option B.