Simplify The Following
1 / √6-√2
Answers
Answer:
Simplify each of the following by rationalising the denominator; 15+√2 (ii) 5+√65-√6 (iii) 7+3√57-3√5 (iv) 2 √3-√52√2+3√3. check-circle. Text Solution. Solution :.
Answer:
\frac{1}{60}(6\sqrt{5}+5\sqrt{6}+\sqrt{330})
60
1
(6
5
+5
6
+
330
)
Step-by-step explanation:
Here, the given expression is,
\frac{1}{\sqrt{6}+\sqrt{5}-\sqrt{11}}
6
+
5
−
11
1
For rationalizing the denominator, multiply both numerator and denominator by √6 + √5 + √11,
=\frac{1}{\sqrt{6}+\sqrt{5}-\sqrt{11}}\times \frac{\sqrt{6}+\sqrt{5}+\sqrt{11}}{\sqrt{6}+\sqrt{5}+\sqrt{11}}=
6
+
5
−
11
1
×
6
+
5
+
11
6
+
5
+
11
=\frac{\sqrt{6}+\sqrt{5}+\sqrt{11}}{(\sqrt{6}+\sqrt{5})^2-(\sqrt{11})^2}=
(
6
+
5
)
2
−(
11
)
2
6
+
5
+
11
=\frac{\sqrt{6}+\sqrt{5}+\sqrt{11}}{6+5+2\times\sqrt{6}\times \sqrt{5}-11}=
6+5+2×
6
×
5
−11
6
+
5
+
11
=\frac{\sqrt{6}+\sqrt{5}+\sqrt{11}}{2\sqrt{30}}=
2
30
6
+
5
+
11
Again for rationalizing the denominator, multiply both numerator and denominator by √30,
=\frac{\sqrt{180}+\sqrt{150}+\sqrt{330}}{60}=
60
180
+
150
+
330
=\frac{6\sqrt{5}+5\sqrt{6}+\sqrt{330}}{60}=
60
6
5
+5
6
+
330
=\frac{1}{60}(6\sqrt{5}+5\sqrt{6}+\sqrt{330})=
60
1
(6
5
+5
6
+
330
)