Question

prove that √3+√5 is irrational​

Answer 1

Answer:

Let √3 + √5 be a rational number , say r

then √3 + √5 = r

On squaring both sides,

(√3 + √5)2 = r2

3 + 2 √15 + 5 = r2

8 + 2 √15 = r2

2 √15 = r2 - 8

√15 = (r2 - 8) / 2

Now (r2 - 8) / 2 is a rational number and √15 is an irrational number .

Since a rational number cannot be equal to an irrational number . Our assumption that √3 + √5 is rational wrong .

Step-by-step explanation:

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Answer 2

: Required Answer

$\longrightarrow$ Given√3 + √5 To prove:√3 + √5 is an irrational number. Let us assume that√3 + √5 is a rational...

➝ Let √3+√5 be a rational number.

➝ A rational number can be written in the form of p/q where p,q are integers. p,q are integers then (p²+2q²)/2pq is a rational number. .

➝ Therefore, √3+√5 is an irrational number.