Can you get a rational number when you compute the difference of two surds Justify answer with an example - Mathematics

Can you get a rational number when you compute the difference of two surds Justify answer with an example

Sum

Yes, the difference of two surds will give a rational number.

Example:

(a) `(5 + sqrt(7)) - (-5 + sqrt(7))` = 10

(b) `(sqrt(11) + 5) - (-3 + sqrt(11))` = 8

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Order of a Surd

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Chapter 2: Real Numbers - Exercise 2.6 [Page 68]

Chapter 2 Real Numbers
Exercise 2.6 | Q 6. (ii) | Page 68

Arrange surds in descending order:

`root(3)(5), root(9)(4), root(6)(3)`

Can you get a pure surd when you find the sum of two surds Justify answer with an example

Can you get a pure surd when you find the difference of two surds Justify answer with an example

Can you get a pure surd when you find the product of two surds Justify answer with an example.

Can you get a pure surd when you find the quotient of two surds Justify answer with an example

Can you get a rational number when you compute the sum of two surds Justify answer with an example

Can you get a rational number when you compute the product of two surds Justify answer with an example

Can you get a rational number when you compute the quotient of two surds Justify answer with an example

Find the odd one out of the following.

If `sqrt(80) = "k"sqrt(5)`, then k =