Question

Q1.Rationalize the denominator a) 8 ÷ 3√2 +√5

Answer 1

Step-by-step explanation:

Given:

$\begin{gathered} \frac{8}{3 \sqrt{2} + \sqrt{5} } \\ \end{gathered}$

To find:

Rationalization

Solution:

Tip: Identity used in denominator

$\begin{gathered}(a-b)(a+b)=a^2-b^2\\\end{gathered}$

To do rationalization of the given number,multiply and divide the number by RF of denominator.

$\begin{gathered} = \frac{8}{3 \sqrt{2} + \sqrt{5} } \times \frac{3 \sqrt{2} - \sqrt{5} }{3 \sqrt{2} - \sqrt{5} } \\ \\ = \frac{8(3 \sqrt{2} - 5)}{( {3 \sqrt{2}) }^{2} - ( { \sqrt{5}) }^{2} } \\ \\ = \frac{8(3 \sqrt{2} - 5)}{18 - 5 } \\ \\ = \frac{8(3 \sqrt{2} - 5) }{13} \\ \end{gathered}$

Final answer:

$\begin{gathered}\red{\frac{8}{3 \sqrt{2} + \sqrt{5} } = \frac{8(3 \sqrt{2} - \sqrt{5} ) }{13}} \\ \end{gathered}$

Answer 2

Step-by-step explanation:

Final answer:

$\begin{gathered}\begin{gathered}\red{\frac{8}{3 \sqrt{2} + \sqrt{5} } = \frac{8(3 \sqrt{2} - \sqrt{5} ) }{13}} \\ \end{gathered}\end{gathered}$