Answer
$$2\sqrt{112}-9\sqrt{175}=-37\sqrt{7}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2\sqrt{112}-9\sqrt{175}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}8\sqrt{7}-45\sqrt{7} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-37\sqrt{7}\end{aligned} $$ | |
| ① | $$ 2 \sqrt{112} =
2 \sqrt{ 4 ^2 \cdot 7 } =
2 \sqrt{ 4 ^2 } \, \sqrt{ 7 } =
2 \cdot 4 \sqrt{ 7 } =
8 \sqrt{ 7 } $$ |
| ② | $$ - 9 \sqrt{175} =
-9 \sqrt{ 5 ^2 \cdot 7 } =
-9 \sqrt{ 5 ^2 } \, \sqrt{ 7 } =
-9 \cdot 5 \sqrt{ 7 } =
-45 \sqrt{ 7 } $$ |
| ③ | Combine like terms |
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