abbey2804 one year ago What is 3 square root 72 in simplest radical form? I got 3 square root 4. But I'm bad at radicals Is this correct?

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1. anonymous

$18\sqrt{2}$

2. mathstudent55

$$\sqrt 4 = 2$$, so a simplified root cannot contain $$\sqrt 4$$. Also, if answer that $$3\sqrt {72} = 3\sqrt 4$$ then you are stating that $$\sqrt {72} = \sqrt 4$$, which is not true. You need to factor out the largest perfect square there is. $$72 = 36 \times 2$$, and $$\sqrt {36} = 6$$ $$3 \sqrt{72} = 3\sqrt {36 \times 2} = 3\sqrt{36}\sqrt 2 = 3 \times 6 \sqrt 2 = 18 \sqrt 2$$