rationalise 3÷3√5+√2
Answers
Answer:
Answer:
Answer:
\begin{gathered} = \frac{3}{3 \sqrt{5} + \sqrt{2} } \\ \\ = \frac{3}{3 \sqrt{5} + \sqrt{2} } \times \frac{3 \sqrt{5} - \sqrt{2} }{3 \sqrt{5} - \sqrt{2} } \\ \\ the \: denominator \: is \: given \: in \: the \: form \\ (a + b)(a - b) = {a}^{2} - {b}^{2} \\ \\ here \: a \: = 3 \sqrt{5} \\ b = \sqrt{2} \\ \\ so \\ = \frac{3(3 \sqrt{5} - \sqrt{2} )}{(3 \sqrt{5} )^{2} - { \sqrt{2} }^{2} } \\ \\ = \frac{9 \sqrt{5} - 3 \sqrt{2} }{(9 \times 5) - 2} \\ \\ = \frac{9 \sqrt{5} - 3 \sqrt{2} }{45 - 2} \\ \\ = \frac{9 \sqrt{5 } - 3 \sqrt{2} }{43} \\ \\ \\ this \: is \: the \: answer....\end{gathered}
=
3
5
+
2
3
=
3
5
+
2
3
×
3
5
−
2
3
5
−
2
thedenominatorisgivenintheform
(a+b)(a−b)=a
2
−b
2
herea=3
5
b=
2
so
=
(3
5
)
2
−
2
2
3(3
5
−
2
)
=
(9×5)−2
9
5
−3
2
=
45−2
9
5
−3
2
=
43
9
5
−3
2
thisistheanswer....