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Simplifying radical expressions calculator
This calculator simplifies expressions involving radicals. The calculator reduces the radical expressions to their simplest form, trying to remove all the radicals from the expression. The calculator shows each step with easy-to-understand explanations.
solution
$$2\sqrt{50}-\sqrt{32}+\sqrt{72}-2\sqrt{8}=8\sqrt{2}$$explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2\sqrt{50}-\sqrt{32}+\sqrt{72}-2\sqrt{8}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}10\sqrt{2}-4\sqrt{2}+6\sqrt{2}-4\sqrt{2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}8\sqrt{2}\end{aligned} $$ | |
| ① | $$ 2 \sqrt{50} =
2 \sqrt{ 5 ^2 \cdot 2 } =
2 \sqrt{ 5 ^2 } \, \sqrt{ 2 } =
2 \cdot 5 \sqrt{ 2 } =
10 \sqrt{ 2 } $$ |
| ② | $$ - \sqrt{32} =
- \sqrt{ 4 ^2 \cdot 2 } =
- \sqrt{ 4 ^2 } \, \sqrt{ 2 } =
- 4 \sqrt{ 2 }$$ |
| ③ | $$ \sqrt{72} =
\sqrt{ 6 ^2 \cdot 2 } =
\sqrt{ 6 ^2 } \, \sqrt{ 2 } =
6 \sqrt{ 2 }$$ |
| ④ | $$ - 2 \sqrt{8} =
-2 \sqrt{ 2 ^2 \cdot 2 } =
-2 \sqrt{ 2 ^2 } \, \sqrt{ 2 } =
-2 \cdot 2 \sqrt{ 2 } =
-4 \sqrt{ 2 } $$ |
| ⑤ | Combine like terms |
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EXAMPLES
example 1:ex 1:
$$\sqrt{125}$$
example 2:ex 2:
$$(7-\sqrt3)(2+\sqrt3)^2$$
example 3:ex 3:
$$2\sqrt{50}-\sqrt{32}+\sqrt{72}-2\sqrt{8}$$
example 4:ex 4:
$$\frac{6}{\sqrt{21}+\sqrt{7}+2\sqrt{3}+2}$$
example 5:ex 5:
$$\frac{1-\sqrt{2}}{1+\sqrt{2}}$$
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