Question

The number obtained on rationalising the denominator of 5/(9-4√2)is?​

Answer 1

Answer:

1.5

Step-by-step explanation:

According to the question , at first we need to rationalise the denominator then there is a new number is formed . We need to find the new number.

So firstly we rationalise the denominator , here the denominator is 9-4√2 . We multiply both numerator and denominator with 9+4√2. Then the numerator will be 5(9+4√2) , denominator will be (9-4√2)(9+4√2).

$\frac{5}{9-4\sqrt{2} } \\\\= \frac{5(9+4\sqrt{2} )}{(9-4\sqrt{2})(9+4\sqrt{2} )} \\\\= \frac{5(9+4\sqrt{2} )}{81-32}\\\\= \frac{45 +20\sqrt{2} }{49}$

$=1.5$

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Answer 2

Answer:

The number obtained by rationalizing the denominator of $\frac{5}{9-4\sqrt{2} }$ = $\frac{45+20\sqrt{2} }{49}$

Step-by-step explanation:

To find,

The number obtained by rationalizing the denominator of $\frac{5}{9-4\sqrt{2} }$

Solution:

The given irrational number is $\frac{5}{9-4\sqrt{2} }$

The rationalizing factor is 9+4√2

To rationalize the denominator, we should multiply the numerator and denominator of the number with the rationalizing factor

$\frac{5}{9-4\sqrt{2} }$ = $\frac{5}{9-4\sqrt{2} } X \frac{9+4\sqrt{2} }{9+4\sqrt{2} }$

= $\frac{5(9+4\sqrt{2} }{9^2 - (4\sqrt{2})^2 }$

= $\frac{45+20\sqrt{2} }{81 - 32}$

= $\frac{45+20\sqrt{2} }{49}$

∴ The number obtained by rationalizing the denominator of $\frac{5}{9-4\sqrt{2} }$ = $\frac{45+20\sqrt{2} }{49}$

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