Question

5. Solve this problem
Please give verified answer with step by step solution​

Answer 1

I hope it may help you

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Answer 2

$\sf\:\boxed{4\sqrt{2} - 3\sqrt{3}}$

Step-by-step explanation:

To Rationalize:

$\sf\:\dfrac{5}{4\sqrt{2} + 3\sqrt{3}}$

Solution:

$\sf\:\frac{5}{4\sqrt{2} + 3\sqrt{3}} \\ \\\implies\sf\:\frac{5 (4 \sqrt{2} - 3 \sqrt{3})}{(4 \sqrt{2} + 3 \sqrt{3})(4 \sqrt{2} - 3 \sqrt{3})}\:\:\: [\because\:a^2-b^2 = (a+b)(a-b)] \\ \\\implies\sf\:\frac{5(4 \sqrt{2} - 3 \sqrt{3})}{ {(4 \sqrt{2})}^{2} - {(3 \sqrt{3})}^{2} } \\ \\\implies\sf\:\frac{5(4 \sqrt{2} - 3 \sqrt{3})}{16.2 - 9.3} \\ \\\implies\sf\:\frac{5(4 \sqrt{2} - 3 \sqrt{3})}{32 - 27} \\ \\ \implies\sf\:\frac{5(4 \sqrt{2} - 3 \sqrt{3})}{5} \\ \\ \implies\sf\:\frac{ \cancel{5}(4 \sqrt{2} - 3 \sqrt{3})}{\cancel{5}} \\ \\\implies\sf\:4 \sqrt{2} - 3 \sqrt{3}$

Therefore, the required answer is 4√2 - 3√3 .

Extra Information:

Rationalizing the denominator is a process by which we can write the irrational denominator in the form of Rational no.

For Rationalizing we use a Conjugate surds or Rationalizing factor which is a factor of the irrational denominator.

e.g conjugate surd of √a is √a and the conjugate surds √a - b is √a + b.