Question

rationalize the denominator7/5✓2-3√3​

Answer 1

Please find the attachment

Answer 2

$\bigstar$ Question:

Rationalise the denominator:

• $\frac{7}{5 \sqrt{2} - 3 \sqrt{3} }$

$\bigstar$Given:

• $\frac{7}{5 \sqrt{2} - 3 \sqrt{3} }$

$\bigstar$To find:

To Rationalise the denominator of :

$\frac{7}{5 \sqrt{2} - 3 \sqrt{3} }$

$\bigstar$ Solution:

$\frac{7}{5 \sqrt{2} - 3 \sqrt{3} }$

$= \frac{7 \times (5 \sqrt{2} + 3 \sqrt{3} )}{(5 \sqrt{2} - 3 \sqrt{3} )(5 \sqrt{2} + 3 \sqrt{3}) }$

$= \frac{(7 \times 5 \sqrt{2}) + (7 \times 3 \sqrt{3} ) }{ {(5 \sqrt{2}) }^{2} - {(3 \sqrt{3}) }^{2} }$

( By using (a+b)(a-b) = a² - b² )

$= \frac{(35 \sqrt{2} + 21 \sqrt{3}) }{(5 \times 5 \times \sqrt{2 }\times \sqrt{2} )(3 \times 3 \times \sqrt{3} \times \sqrt{3} ) }$

$= \frac{35 \sqrt{2} + 21 \sqrt{3} }{(25 \times 2) - (9 \times 3)}$

$= \frac{(35 \sqrt{2} + 21 \sqrt{3}) }{50 - 27}$

$= \frac{35 \sqrt{2} + 21 \sqrt{3} }{23}$

$\bigstar$Answer:

$\frac{35 \sqrt{2} + 21 \sqrt{3} }{23}$

= $\frac{ 7 (5\sqrt{2} + 3 \sqrt{3})}{23}$

$\blacksquare$ Formulas used:

• ( a + b ) ( a - b ) = a² - b²
• √a × √a = a