Question

4√3+5√2÷√48+√18....(Rationalise the denominator)

solve it plss..
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Answer 1

Answer:

Answer = 3/5 ................

Answer 2

Answer:

$\red{\boxed{\bf{\frac{9 + 4\sqrt{6}}{15}}}}$

To Rationalize:

$\dfrac{4\sqrt{3} + 5 \sqrt{2} }{ \sqrt{48} + \sqrt{18}}$

Solution:

$\sf\:\frac{4\sqrt{3} + 5 \sqrt{2}}{\sqrt{48} + \sqrt{18}} \\ \\\implies\sf\:\frac{4 \sqrt{3} + 5 \sqrt{2} }{ \sqrt{16 \times 3} + \sqrt{9 \times 2} } \\ \\\implies\sf\:\frac{4 \sqrt{3} + 5 \sqrt{2} }{ 4\sqrt{3} + 3 \sqrt{2} } \\ \\\implies\sf\:\frac{(4 \sqrt{3} + 5 \sqrt{2} )(4 \sqrt{3} - 3 \sqrt{2})}{(4 \sqrt{3} + 3 \sqrt{2})(4 \sqrt{3} - 3 \sqrt{2})}\:\:\: [\because\:a^2-b^2 = (a+b)(a-b)] \\ \\\implies\sf\:\frac{4 \sqrt{3} \times 4 \sqrt{3} - 4 \sqrt{3} \times 3 \sqrt{2} + 5 \sqrt{2} \times 4 \sqrt{3} - 5 \sqrt{2} \times 3 \sqrt{2} }{ {(4 \sqrt{3})}^{2} - {(3 \sqrt{2})}^{2} } \\ \\\implies\sf\:\frac{48 - 12 \sqrt{6} + 20 \sqrt{6} - 30}{48 - 18} \\ \\\implies\sf\:\frac{48 - 30 + 20 \sqrt{6} - 12 \sqrt{6} }{30} \\ \\ \implies\sf\:\frac{18 + 8 \sqrt{6} }{30} \\ \\ \implies\sf\:\frac{2(9 + 4 \sqrt{6})}{30} \\ \\\implies\sf\:\frac{9 + 4 \sqrt{6} }{15}$

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.