Leadership

Mathematics

Nine Standard >> Operations on surds | Part-2

Click the green "Start" button for MCQ.
Leadership

 

Multiplication operation on surds

 

Multiplication involving surds, also known as radicals, follows specific rules to simplify and perform the operation. Surds are expressions that include a radical symbol (√) and a number or variable under the radical. Here's how multiplication of surds works:

\(\sqrt{a}+\sqrt{b}\) ≠ \(\sqrt{ab}\)
\(\sqrt{2}+\sqrt{3}\) ≠ \(\sqrt{5}\)

\(\sqrt{a}.\sqrt{b}\)= \(\sqrt{ab}\)
\(\sqrt{2}.\sqrt{3}\)= \(\sqrt{6}\)

Surds of the same order can be multiplied

\(\sqrt[n]{x}.\sqrt[n]{y}=x^{\frac{1}{n}}.y^{\frac{1}{n}}=(xy)^{\frac{1}{n}}=\sqrt[n]{xy}\)
\(\sqrt[n]{x}.\sqrt[m]{y}=x^{\frac{1}{n}}.y^{\frac{1}{m}}=x^{\frac{m}{nm}}.y^{\frac{n}{nm}}\)
      \(=(x^{m})^{\frac{1}{nm}}.(y^{n})^{\frac{1}{nm}}\)=\((x^{m}.y^{n})^{\frac{1}{nm}}\)
        =\(\sqrt[mn]{x^{m}.y^{n}}\)


Example:

\(\sqrt[3]{2} \times \sqrt{3}=2^{\frac{1}{3}}.3^{\frac{1}{2}}\)
              =\(2^{\frac{1 \times 2}{3 \times 2}}.3^{\frac{1 \times 3}{2 \times 3}}\) [ LCM of 2 &3 is 6]
              =\(2^{\frac{2}{6}}.3^{\frac{3}{6}}\)
              =\(\sqrt[6]{2^{2}}.\sqrt[6]{3^{3}}\)
              =\(\sqrt[6]{4 \times 27}\)
              =\(\sqrt[6]{108}\)

Leadership
Hand drawn

Hide

Forgot your password?

Close

Error message here!

Hide

Lost your password? Please enter your email address. You will receive a link to create a new password.

Back to log-in

Close