Question

given that root 5 = 2.236068,find the value of 87/7-2 root 5

Answer 1

Ans = 34.416408

multiply numerator and denominator by
$7 + 2 \sqrt{5}$
((87)×(7+2√5))/(7-2√5)*(7+2√5)

((87)×(7+2√5))/(49-20)

((87)×(7+2√5))/3

3 × (7+2√5)

21 + 6√5

21 + 13.416408

34.416408

Answer 2

Step-by-step explanation:

$\bf \underline{Given-}$

$\textsf{√5 = 2.236058}$

$\bf \underline{To \: find-}$

$\rm {the \: value \: of : \: \frac{87}{7 - 2 \sqrt{5} } }$

$\bf \underline{Solution-}$

$\textsf{Rationalising the denominator, we get}$

$\frac{87}{7 - 2 \sqrt{5} }$

$= \frac{87}{7 - 2 \sqrt{5} } \times \frac{7 + 2 \sqrt{5} }{7 + 2 \sqrt{5} }$

$= \frac{87(7 + 2 \sqrt{5} )}{(7 - 2 \sqrt{5})(7 + 2 \sqrt{5}) }$

$= \frac{87(7 + 2 \sqrt{5} )}{(7 {)}^{2} - (2 \sqrt{5} {)}^{2} }$

$= \frac{87(7 + 2 \sqrt{5} )}{49 - 20}$

$= \frac{87(7 + 2 \sqrt{5} )}{29}$

$= 3(7 + 2 \times 2.236068)$

$= 3 \times 11.472136$

$= 34.316408$

$\bf{ \underline{Hence, the \: value \: of \: : \frac{87}{7 - 2 \sqrt{5} } \: is \: 34.416408 }} .$