Question

an equivalent Expression of 5÷7+4√5 after rationalize the denominator is​

Answer 1

Answer:

After rationalize the denominator is 31.

Step-by-step explanation:

Given expression is $\frac{5}{7 + 4 \sqrt{5} }$

Here we want to rationalize it.

Denominator is $(7 + 4 \sqrt{5} )$

and numirator is 5.

So, we are multiplying denominator and numinator by$7 - 4 \sqrt{5}$

We get,

$\frac{5 \times (7 - 4 \sqrt{5} )}{(7 + 4 \sqrt{5})(7 - 4 \sqrt{5)} }$

$\frac{35 - 20 \sqrt{5} }{ {7}^{2} - {(4 \sqrt{5}) }^{2} } = \frac{35 - 20 \sqrt{5} }{49 - 80} = \frac{35 - 20 \sqrt{5} }{ - 31} = \frac{ - 35 + 20 \sqrt{5} }{31}$

After rationalize the denominator is 31.

Here applied formula is ${x}^{2} - {y}^{2} = (x + y)(x - y)$