Question
Multiply and express in simplest radical form:
left bracket, 1, minus, 2, square root of, 24, end square root, right bracket, left bracket, minus, 2, plus, square root of, 6, end square root, right bracket
left bracket, 1, minus, 2, square root of, 24, end square root, right bracket, left bracket, minus, 2, plus, square root of, 6, end square root, right bracket
Answers
Answered by
GPT 3.5
To simplify this expression, we first need to find the square roots of 24 and 6:
√24 = √(4 * 6) = 2√6
√6 is already simplified
Now we can substitute these values back into the expression:
(1 - 2√6)(-2 + √6)
= 1*(-2) + 1*(√6) - 2√6*(-2) - 2√6*(√6)
= -2 + √6 - (-4√6) - 2√6
= -2 + √6 + 4√6 - 2√6
= 2√6 - 2
Therefore, the expression simplifies to: 2√6 - 2
√24 = √(4 * 6) = 2√6
√6 is already simplified
Now we can substitute these values back into the expression:
(1 - 2√6)(-2 + √6)
= 1*(-2) + 1*(√6) - 2√6*(-2) - 2√6*(√6)
= -2 + √6 - (-4√6) - 2√6
= -2 + √6 + 4√6 - 2√6
= 2√6 - 2
Therefore, the expression simplifies to: 2√6 - 2
Answer
are you sure
Answered by
GPT 3.5
Apologies for the mistake in my previous response. Let's reevaluate the expression:
(1 - 2√24)(-2 + √6)
= 1*(-2) + 1*(√6) - 2√24*(-2) - 2√24*(√6)
= -2 + √6 + 4√24 - 2√144
= -2 + √6 + 4√24 - 2(12)
= -2 + √6 + 4√24 - 24
= -26 + √6 + 4√24
Therefore, the expression simplifies to: -26 + √6 + 4√24
(1 - 2√24)(-2 + √6)
= 1*(-2) + 1*(√6) - 2√24*(-2) - 2√24*(√6)
= -2 + √6 + 4√24 - 2√144
= -2 + √6 + 4√24 - 2(12)
= -2 + √6 + 4√24 - 24
= -26 + √6 + 4√24
Therefore, the expression simplifies to: -26 + √6 + 4√24