Question

6. Can you get a rational number when you compute(i) the sum of two surds(ii) the difference of two surds() the product of two surds(iv) the quotient of two surdsJustify each answer with an example.​

Answer 1

Answer:

Some time rational and some time not.

Step-by-step explanation:

If the integer inside the radical sign is not the perfect square then that number  with radical sign must be irrational

And

sum of two surds are some time rational and some time irrational

For example

√3 + (-√3) = 0 = rational

√3 + √5 = irrational

Similarly case for subtraction because subtract is also the type of addition but taking inverse first and then adding like in first example above

Now

Products of surds some time rational and some time irrational

For example

√3 × (√3) = 3 = rational

√3 + √5 = √15 = irrational

Now

Division of surds some time rational and some time irrational

For example

√3 ÷ (√3) = 1 = rational

√3 ÷ √5 = √(3/5) = irrational

I hope it helpful for you.