Question

find the positive square root of 3 +root 5​

Answer 1

Answer:

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