Question

√(3+√5)=?
ans=√(7/2)-√(1/2)
explanation=?​

Answer 1

Answer:

$\frac{\sqrt{10} }{2} + \frac{\sqrt{2} }{2}$

Step-by-step explanation:

SEEMS LIKE THE ANSWER MUST BE DIFFERENT AS A PLUS SIGN IN THE ROOT CAN NEVER YIELD A MINUS SIGN IN THE ANSWER

$\sqrt{3+\sqrt{5} }$

Now if we multiply and divide by 2, we get

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

taking 2 inside the root, we get

$\frac{\sqrt{12+4\sqrt{5} } \\}{2}$

taking only 2 as a factor of 4 inside the root

$\frac{\sqrt{12+2\sqrt{20} } \\}{2}$

if we see carefully, the expression in the root is a perfect square, therefore if we factorize it, we get

$\frac{\sqrt{10 + 2 +2\sqrt{20} } \\}{2}$

$\frac{\sqrt{( 10+2)^{2} } \\}{2}$

therefore, finally removing the brackets, we get our answer as

$\frac{\sqrt{10} }{2} + \frac{\sqrt{2} }{2}$ ANSWER

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