3+sqrt(5)= Option 1: sqrt(2)+1 Option 2: sqrt(5/2)+sqrt(1/2) Option 3: sqrt(7/2)-sqrt(1/2) Option 4: sqrt(9/2)-sqrt(3/2)

Answer: sqrt(5/2)+sqrt(1/2). Solution: To solve this easily, we can go through the options and square the given options to see if they equate 3+5 Look at the second option. We know that (a+b)^2=a^2+b^2+2ab Squaring the second option, we'll get: 5/2+1/2+2(sqrt(5/2))(sqrt(1/2)) 6/2+25/2=3+5

Algebra Indices

Medium

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

$\sqrt{2}+1$

$\sqrt{\frac{5}{2}}+\sqrt{\frac{1}{2}}$

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

$\sqrt{\frac{9}{2}}-\sqrt{\frac{3}{2}}$

✅ Correct Option: 2

To solve this easily, we can go through the options and square the given options to see if they equate $3+\sqrt5$ Look at the second option. We know that $(a+b)^2=a^2+b^2+2ab$ Squaring the second option, we'll get: $\frac{5}{2}+\frac{1}{2}+2(\sqrt{\frac{5}{2}})(\sqrt{\frac{1}{2}})$ $\frac{6}{2}+\frac{2\sqrt5}{2}=3+\sqrt5$

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

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