Math, asked by anupsaji1994, 1 year ago

If m= 7-4√3, then √(m+1/√m)=?

Answers

Answered by Anonymous
0
hope it will help you
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Answered by harendrachoubay
0

\dfrac{\sqrt{m}+1}{\sqrt{m}} =\sqrt{3} (\sqrt{3} +1)

Step-by-step explanation:

We have,

m=7-4\sqrt{3}

To find, \dfrac{\sqrt{m}+1}{\sqrt{m}} =?

m=7-4\sqrt{3}

m=2^{2} +\sqrt{3} ^{2}-2(2)(\sqrt{3})=(2-\sqrt{3})^{2}

\dfrac{\sqrt{m}+1}{\sqrt{m}} =\dfrac{\sqrt{(2-\sqrt{3})^{2}}+1}{\sqrt{(2-\sqrt{3})^{2}}}

=\dfrac{2-\sqrt{3}+1}{2-\sqrt{3}}}

=\dfrac{3-\sqrt{3}}{2-\sqrt{3}}}

Rationalising numerator and denominator, we get

=\dfrac{3-\sqrt{3}}{2-\sqrt{3}}}\times \dfrac{2+\sqrt{3}}{2+\sqrt{3}}

=({3-\sqrt{3})(\dfrac{2+\sqrt{3})}{2^2-\sqrt{3}^2}}}

=6+3\sqrt{3} -2\sqrt{3}-3

=3+\sqrt{3}=\sqrt{3} (\sqrt{3} +1)

Hence, \dfrac{\sqrt{m}+1}{\sqrt{m}} =\sqrt{3} (\sqrt{3} +1)

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