Question

Which value is equal to √(354−√424) ?
A) √116
B) -11√6
C) √-6
D) √6

Answer 1

To evaluate √(354−√424), we first need to simplify the expression inside the square root. The final answer is √354 - 2√53.

Step-by-step explanation:

To evaluate √(354−√424), we first need to simplify the expression inside the square root. Starting with the inner square root, √424, we can determine its value by factoring it: √(2x212) = √(2x2x53) = √(2x2)x√53 = 2√53. Substituting this value back into the original expression, we have √(354−2√53).

Let's now simplify the outer square root. Remember that √a - √b is not equal to √(a - b); instead, it represents two separate square roots being subtracted. Applying this concept here, we have √354 - 2√53.

Since there are no like terms, we cannot simplify any further. Therefore, the final answer is: √(354−√424) = √354 - 2√53.