Question

Positive sqare root of 3+√5

Answer 1

Step-by-step explanation:

I assume that you want the square roots, not cube roots, fourth roots ….

So, we want to find y given that:

y2=3+5–√=2+1+5–√=2+21+5√2

Now, 1+5√2 is a well-known mathematical value; it is called the golden ratio and designated using ϕ , so:

y2=2+2ϕ=2(1+ϕ)

One of ϕ′s properties is that 1+ϕ=ϕ2 , so:

y2=2ϕ2⇒y=±2–√ϕ

=±2√+10√2

≈±2.288245611