Rationalise 4/root2.
Answers
Answer:
The rationalization of \frac{4\sqrt{3}+5\sqrt{2}}{4\sqrt{3}+3\sqrt{2}}
4
3
+3
2
4
3
+5
2
is \frac{9+4\sqrt{6}}{15}
15
9+4
6
Step-by-step explanation:
Given : 4 root 3 +5 root 2/4 root 3+3 root 2
To find : Rationalize the given expression?
Solution :
The given expression is \frac{4\sqrt{3}+5\sqrt{2}}{4\sqrt{3}+3\sqrt{2}}
4
3
+3
2
4
3
+5
2
Rationalizing the expression by multiplying and dividing denominator with opposite sign,
=\frac{4\sqrt{3}+5\sqrt{2}}{4\sqrt{3}+3\sqrt{2}}\times \frac{4\sqrt{3}-3\sqrt{2}}{4\sqrt{3}-3\sqrt{2}}=
4
3
+3
2
4
3
+5
2
×
4
3
−3
2
4
3
−3
2
The denominator is multiplied by using the formula,
\bold{(a+b)(a-b)=a^{2}-b^{2}}(a+b)(a−b)=a
2
−b
2
=\frac{(4\sqrt{3})^2-(4\sqrt{3})(3\sqrt2)+(5\sqrt{2})(4\sqrt{3})-(5\sqrt{2})(3\sqrt{2})}{(4\sqrt{3})^2-(3\sqrt{2})^2}=
(4
3
)
2
−(3
2
)
2
(4
3
)
2
−(4
3
)(3
2
)+(5
2
)(4
3
)−(5
2
)(3
2
)
=\frac{48-12\sqrt{6}+20\sqrt{6}-30}{48-18}=
48−18
48−12
6
+20
6
−30
=\frac{9+4\sqrt{6}}{15}=
15
9+4
6
Therefore, The rationalization of \frac{4\sqrt{3}+5\sqrt{2}}{4\sqrt{3}+3\sqrt{2}}
4
3
+3
2
4
3
+5
2
is \frac{9+4\sqrt{6}}{15}
15
9+4
6
Answer:
Answer is :- 2√2
Hope! answer is helpful for you....
