Question

What denominator do we obtain after rationalising the denominator of 4/7root5-5root7

Answer 1

ANSWER:

$\dfrac{2(7 \sqrt{5} + 5 \sqrt{7}) }{35}$

GIVEN:

$\dfrac{4}{7 \sqrt{5} - 5 \sqrt{7} }$

TO FIND:

• Value of above expression.

SOLUTION:

$= \dfrac{4}{7 \sqrt{5} - 5 \sqrt{7} } \\ \\ = \frac{4}{7 \sqrt{5} - 5 \sqrt{7} } \times \frac{7 \sqrt{5} + 5 \sqrt{7} }{7 \sqrt{5} + 5 \sqrt{7} } \\ \\ = \frac{4(7 \sqrt{5} + 5 \sqrt{7}) }{(7 \sqrt{5}) {}^{2} - ( \sqrt{7}) {}^{2} } \\ \\ = \frac{4(7 \sqrt{5} + 5 \sqrt{7} )}{245 - 175} \\ \\ = \frac{2(7 \sqrt{5} + 5 \sqrt{7} ) }{35}$

NOTE:

• In nationalisation we have to multiply with a number so that the root from the denominator get removed.
• Here we see that in denominator a identity is used that is (a+b)(a-b)= a²-b²
• Some important formulas:
• (a+b)² = a²+b²+2ab
• (a-b)² = a²+b²-2ab