Question

61 simplify the expression $10\sqrt{7} - \sqrt{28} + 6\sqrt{180}$

Explanation:

Step1: Simplify $\sqrt{28}$

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

Step2: Simplify $6\sqrt{180}$

Factor 180: $180 = 36\times5$. So $\sqrt{180}=\sqrt{36\times5}=\sqrt{36}\times\sqrt{5}=6\sqrt{5}$. Then $6\sqrt{180}=6\times6\sqrt{5}=36\sqrt{5}$.

Step3: Substitute back and combine like terms

Original expression: $10\sqrt{7}-\sqrt{28}+6\sqrt{180}$ becomes $10\sqrt{7}-2\sqrt{7}+36\sqrt{5}$. Combine $10\sqrt{7}-2\sqrt{7}$: $(10 - 2)\sqrt{7}=8\sqrt{7}$. So the simplified expression is $8\sqrt{7}+36\sqrt{5}$.

Answer:

$8\sqrt{7} + 36\sqrt{5}$