Nine Standard >> Operations on surds | Part-1

Operation of surds

Addition of Surds:

Do you think ? \(\sqrt{2}+\sqrt{3}\)=\(\sqrt{2+3}\)=\(\sqrt{5}\)

We know,

\(\sqrt{2}\)=1.414
\(\sqrt{3}\)=1.732
\(\sqrt{5}\)=2.236

Now, \(\sqrt{2}+\sqrt{3}\)=1.414+1.732=3.146

So,  \(\sqrt{2}+\sqrt{3}\) ≠ \(\sqrt{5}\)

Only similar surds can add i.e

\(\sqrt{a}+2\sqrt{a}+5\sqrt{a}\)
\(=(1+2+5)\sqrt{a}=8\sqrt{a}\)

\(3\sqrt[3]{5}+2\sqrt[3]{5}\)
\(=(3+2)\sqrt[3]{5}=5\sqrt[3]{5}\)

Substruction of Surds:

\(8\sqrt{2}-2\sqrt{2}\)=\((8-2)\sqrt{2}=6\sqrt{2}\)

\(3\sqrt{2}-5\sqrt{3}+7\sqrt{2}+2\sqrt{3}\)
\(=(3+7)\sqrt{2}-(5-2)\sqrt{3}\)
\(=10\sqrt{2}-3\sqrt{3}\)

Multiplication of Surds:

\(\sqrt{5}\times\sqrt{2}=\sqrt{5\times2}=\sqrt{10}\)