Question

please help me in rationalizing these 2 ​

Answer 1

Step-by-step explanation:

1st solution:

$\frac{1}{ \sqrt{7} } + \frac{1}{ \sqrt{3} } - \frac{1}{ \sqrt{2} }$

• 1st we Rationalise all the denominator.
• 2nd we arrange all according to the given question and simplify and last we get the answer.

$First \: term: \frac{1}{ \sqrt{7} }$

Rationalising factor of√a is√a . To rationalise the denominator of 1/√2, we multiply this by √7/√7.

we get,

$∴ \: \: \frac{1}{ \sqrt{7} } = \frac{1}{ \sqrt{7} } \times \frac{ \sqrt{7} }{ \sqrt{7} } = \frac{ \sqrt{7} }{ \sqrt{7 \times 7} } = \red{\frac{ \sqrt{7} }{7} }$

$Second \: term: \: \frac{1}{ \sqrt{3} }$

Rationalising factor of√a is √a. To rationalise the denominator of 1/√3, we multiply this by √3/√3.

we get,

$∴ \: \frac{1}{ \sqrt{3} } = \frac{1}{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } = \frac{ \sqrt{3} }{ \sqrt{3 \times 3} } = \red{ \frac{ \sqrt{3}} {3 } }$

$Third \: term: \frac{1}{ \sqrt{2} }$

Rationalising factor of √a is√a. To rationalise the denominator of 1/√2, we multiply this by √2/√2

we get,

$∴ \: \frac{1}{ \sqrt{2} } = \frac{1}{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} } = \frac{ \sqrt{2} }{ \sqrt{2 \times 2} } = \red{\frac{ \sqrt{2} }{2} }$

$Hence, \frac{1}{ \sqrt{7} } + \frac{1}{ \sqrt{3} } - \frac{1}{ \sqrt{2} }$

$= \red{ \frac{ \sqrt{7} }{7} + \frac{ \sqrt{3} }{3} - \frac{ \sqrt{2} }{2} }$

$= 0.248207961 \: ans \: in \: Approx$

2nd solution:

$\frac{1}{ \sqrt{7} + \sqrt{3} - \sqrt{2} }$

In attachment I have answered this problem.⬆️⤴️

I think 1st one question is wrong because denominator is not rationalised.