The value of √2+√3/√(2+√3)
Answers
The value of \sqrt{\dfrac{2+\sqrt{3}}{2-\sqrt{3}} }
2−
3
2+
3
is 3.73.
Step-by-step explanation:
We have,
\sqrt{\dfrac{2+\sqrt{3}}{2-\sqrt{3}} }
2−
3
2+
3
To find, the value of \sqrt{\dfrac{2+\sqrt{3}}{2-\sqrt{3}}}
2−
3
2+
3
= ?
Rationalising numerator and denominator, we get
\sqrt{\dfrac{2+\sqrt{3}}{2-\sqrt{3}}\times\dfrac{2+\sqrt{3}}{2+\sqrt{3} }
=\sqrt{\dfrac{(2+\sqrt{3})^{2} }{2^{2} -(\sqrt{3})^{2} }
[ ∵ a^{2} -b^{2} =(a+b)(a-b)a
2
−b
2
=(a+b)(a−b)
=\sqrt{\dfrac{(2+\sqrt{3})^{2} }{4 -3}
=\sqrt{\dfrac{(2+\sqrt{3})^{2} }{1}
=2+\sqrt{3}=2+
3
= 2 + 1.73 [∵ \sqrt{3}
3
= 1.73]
= 3.73
Hence, the value of \sqrt{\dfrac{2+\sqrt{3}}{2-\sqrt{3}} }
2−
3
2+
3
is 3.73
Answer:
answer is 1.
Step-by-step explanation:
just rationalise the denominator and get this answer.
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