Question

express in simplest radical form.

$6\sqrt{175} + 7\sqrt{28}$

answer
attempt 1 out of 2

text box submit answer

radical symbol button

Explanation:

Step1: Simplify $\sqrt{175}$

Factor 175: $175 = 25\times7$. So, $\sqrt{175}=\sqrt{25\times7}=\sqrt{25}\times\sqrt{7}=5\sqrt{7}$. Then $6\sqrt{175}=6\times5\sqrt{7}=30\sqrt{7}$.

Step2: Simplify $\sqrt{28}$

Factor 28: $28 = 4\times7$. So, $\sqrt{28}=\sqrt{4\times7}=\sqrt{4}\times\sqrt{7}=2\sqrt{7}$. Then $7\sqrt{28}=7\times2\sqrt{7}=14\sqrt{7}$.

Step3: Add the two simplified terms

$30\sqrt{7}+14\sqrt{7}=(30 + 14)\sqrt{7}=44\sqrt{7}$.

Answer:

$44\sqrt{7}$