Question

√3+√5 is rational or irrational​

Answer 1

Answer:

Irrational

Step-by-step explanation:

√3+√5 is irrational but we take that as a rational

(√3+√5)^2=k^2

3+5=k^2

8=k^2

2√2=k

So we can say that √3+√5is an irrational no

Answer 2

Hey mate!❤️

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- Key points to know wheter a given number is rational or irrational!

• A number is said to be irrational when it is not expressed in form of P/q where , p & q are integers and q is a non zero number!

• Non terminating , non - repeating decimals are also irrational number but not so it is a rational number!

• Also , when a given (√) number is not a perfect square , It will be an irrational number .

- Here ,

√3 + √5 is not a perfect square , so we can't express it in p/q form .

- Hence ,

√3+√5 is an irrational

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We can also prove it by following steps :

Let the required number be x .

Then ,

x = √3 - √5

Squaring both sides ,

x² = (√3-√5)²

x² = 3+5-2√15

x² = 8-2√15

x² + 8 = 2√15

(x²+8)/2 = √15

So , √15 is an irrational number .

Hence Proved ✔