Rationalise the denominators of the following:
(i) \(\frac{1 }{ \sqrt{7 }}\)
(ii) \(\frac{1 }{ \sqrt{7 }-\sqrt6}\)
(iii) \(\frac{1 }{ \sqrt{5}+\sqrt2}\)
(iv) \(\frac{1 }{ \sqrt{7}-2}\)
Rationalise the denominators of the following:
(i) \(\frac{1 }{ \sqrt{7 }}\)
(ii) \(\frac{1 }{ \sqrt{7 }-\sqrt6}\)
(iii) \(\frac{1 }{ \sqrt{5}+\sqrt2}\)
(iv) \(\frac{1 }{ \sqrt{7}-2}\)
Solution and Explanation
(i) \(\frac{1 }{ \sqrt{7 }}\) =\(\frac{1}{\sqrt7}=\frac{1}{\sqrt7} ×\frac{ √7 }{√7}\)
= \(\frac{ √7 }{√7}\)
(ii) \(\frac{1 }{ \sqrt{7 }-\sqrt6}\)
\(= \frac{1}{ (√7 + √6)} ×\frac{(√7 - √6)}{(√7 + √6)}\)
= \(\frac{(√7 - √6)}{7 - 6}=\sqrt7+\sqrt6\)
(iii) \(\frac{1 }{ \sqrt{7}-2}\)
\(\frac{\sqrt5+\sqrt2}{3}\)
(iv) \(\frac{1 }{ \sqrt{7}-2}\)
\(=\frac{\sqrt7+2}{7-2}=\frac{\sqrt7+2}{3}\)
Top CBSE Class IX Mathematics Questions
Top CBSE Class IX Questions
- The following table gives the lifetimes of 400 neon lamps:
Length (in hours)
Number of lamps
300 − 400
14
400 − 500
56
500 − 600
60
600 − 700
86
700 − 800
74
800 − 900
62
900 − 1000
48
(i) Represent the given information with the help of a histogram.
(ii) How many lamps have a lifetime of more than 700 hours? - Give an example to show that even as a young girl Santosh was not ready to accept anything unreasonable.
- Where was Abdul Kalam’s house?
- What do you think Dinamani is the name of? Give a reason for your answer.
Why was Santosh sent to the local school?