Question

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Answer 1

★Solution★

$(\sqrt{ \frac{2}{5} } + \sqrt{ \frac{3}{2} } )( \sqrt{2} + \sqrt{3} )$

On opening the brackets, we get:

$⇒ \sqrt{ \frac{4}{5} } + \sqrt{ \frac{6}{2} } + \sqrt{ \frac{6}{5} } + \sqrt{ \frac{9}{2} }$

Now, ∵ √4=2 and √9=3

$⇒ \frac{2}{ \sqrt{5} } + \frac{ \sqrt{6} }{ \sqrt{2} } + \frac{ \sqrt{6} }{ \sqrt{5} } + \frac{3}{ \sqrt{2} }$

On rationalising the denominators of each term, we get:

$⇒ \frac{2 \sqrt{5} }{5} + \sqrt{3} + \frac{ \sqrt{30} }{5} + \frac{3 \sqrt{2} }{2}$

On Taking L.C.M. of 1, 2, and 5, i.e., 10 and multiplying both numerators and denominators of each term, we get:

$⇒ \frac{4 \sqrt{5} + 10 \sqrt{3} + 2 \sqrt{30} + 15 \sqrt{2} }{10}$

Or simply, the expression can be written as:

$or \: \: \: \frac{2 \sqrt{5} + \sqrt{30} }{5} + \frac{3 \sqrt{2} }{2} + \sqrt{3}$

Which is the value of the given expression

Now,

After substituting, √5=2.236, √2=1.414 and √3=1.732

$⇒ ( \sqrt{ \frac{2}{5} } + \sqrt{ \frac{3}{2} } )( \sqrt{2} + \sqrt{3} )≈ 5.843$

Answer 2

Answer:

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