Question

express in simplest radical form.
$-sqrt{24} - sqrt{150}$

Explanation:

Step1: Factor the radicands

Factor 24 and 150 into products of perfect squares and other factors.
For \( \sqrt{24} \), we have \( 24 = 4\times6 \), where 4 is a perfect square.
For \( \sqrt{150} \), we have \( 150 = 25\times6 \), where 25 is a perfect square.
So, \( -\sqrt{24}-\sqrt{150}=-\sqrt{4\times6}-\sqrt{25\times6} \)

Step2: Use the property of square roots

Use the property \( \sqrt{ab}=\sqrt{a}\times\sqrt{b} \) (where \( a\geq0,b\geq0 \)) to simplify the radicals.
\( -\sqrt{4\times6}-\sqrt{25\times6}=-\sqrt{4}\times\sqrt{6}-\sqrt{25}\times\sqrt{6} \)
Since \( \sqrt{4} = 2 \) and \( \sqrt{25}=5 \), we substitute these values in:
\( - 2\sqrt{6}-5\sqrt{6} \)

Step3: Combine like terms

Combine the two terms with \( \sqrt{6} \).
\( -2\sqrt{6}-5\sqrt{6}=(-2 - 5)\sqrt{6}=-7\sqrt{6} \)

Answer:

\( -7\sqrt{6} \)