Question

express in simplest radical form.

$9\sqrt{150} + \sqrt{24}$

answer
attempt 1 out of 2

input box submit answer button

radical symbol button

Explanation:

Step1: Simplify \( \sqrt{150} \)

Factor 150: \( 150 = 25 \times 6 \), so \( \sqrt{150} = \sqrt{25 \times 6} = \sqrt{25} \times \sqrt{6} = 5\sqrt{6} \)
Then \( 9\sqrt{150} = 9 \times 5\sqrt{6} = 45\sqrt{6} \)

Step2: Simplify \( \sqrt{24} \)

Factor 24: \( 24 = 4 \times 6 \), so \( \sqrt{24} = \sqrt{4 \times 6} = \sqrt{4} \times \sqrt{6} = 2\sqrt{6} \)

Step3: Add the simplified radicals

\( 9\sqrt{150} + \sqrt{24} = 45\sqrt{6} + 2\sqrt{6} = (45 + 2)\sqrt{6} = 47\sqrt{6} \)

Answer:

\( 47\sqrt{6} \)