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

Sum

Yes we can get a surd.

Example:

(a) `sqrt(75) - sqrt(48) = sqrt(25 xx 3) - sqrt(16 xx 3) = (5 - 4)sqrt(3) = sqrt(3)`

(b) `sqrt(98) - sqrt(72) = sqrt(49 xx 2) - sqrt(36 xx 2) = (7 - 6)sqrt(2) = sqrt(2)`

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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 5. (ii) | Page 68

Arrange surds in descending order:

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

Arrange surds in descending order:

`root(2)root(3)(5), root(3)root(4)(7), sqrt(sqrt(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 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 difference 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

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