Adding and Subtracting Square Roots

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Lesson

Practice Problems

\(\textbf{1)}\) \(3\sqrt{5}+6\sqrt{5}\)

 

\(\textbf{2)}\) \(7\sqrt{3}-3\sqrt{3}\)

 

\(\textbf{3)}\) \(5\sqrt{7}+6\sqrt{7}\)

 

\(\textbf{4)}\) \(3\sqrt{2}-7\sqrt{2}\)

 

\(\textbf{5)}\) \(2\sqrt{5}+3\sqrt{5}+4\sqrt{5}\)

 

\(\textbf{6)}\) \(\sqrt{3}+4\sqrt{3}\)

 

\(\textbf{7)}\) \(5\sqrt{6}-3\sqrt{6}+8\sqrt{6}\)

 

\(\textbf{8)}\) \(3\sqrt{2}+5\sqrt{5}+8\sqrt{2}-2\sqrt{5}\)

 

\(\textbf{9)}\) \(6\sqrt{3}-3\sqrt{2}+8\sqrt{3}-\sqrt{2}\)

 

 

Challenge Problems

\(\textbf{10)}\) \( 2\sqrt{12}+5\sqrt{27} \)

 

\(\textbf{11)}\) \( 5\displaystyle\sqrt{3}-\displaystyle\sqrt{27} \)Link to Youtube Video Solving Question 11

 

\(\textbf{12)}\) \( \displaystyle\sqrt{30}+\displaystyle\sqrt{5} \)Link to Youtube Video Solving Question 12

 

See Related Pages\(\)

\(\bullet\text{ Simplifying Square Roots}\)
\(\,\,\,\,\,\,\,\,\sqrt{32}=4\sqrt{2}…\)
\(\bullet\text{ Multiplying Square Roots}\)
\(\,\,\,\,\,\,\,\, \sqrt{5} \cdot \sqrt{125} …\)
\(\bullet\text{ Dividing Square Roots}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{\sqrt{12}}{\sqrt{3}}…\)

 

In Summary

Adding and subtracting square roots is a mathematical operation that involves combining square roots that have the same radicand (the number inside the square root symbol). To add or subtract square roots, we first need to make sure that the radicands are the same. We can combine all terms with the same radicand by adding the coefficients.

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