Question

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

Answer 1

87×7-87×2√5 /20
609-87×4.5/20
609-391.5/20
217.5/20
10.875

Answer 2

Step-by-step explanation:

$\bf \underline{Given-}$

$\textsf{√5 = 2.236058}$

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

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

$\bf \underline{Solution-}$

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

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

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

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

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

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

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

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

$= 3 \times 11.472136$

$= 34.316408$

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