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

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

Sum

Yes we can get a surd.

Example:

(a) `sqrt(55) ÷ sqrt(5) = sqrt(11 xx 5)/sqrt(5) = sqrt(11)`

(b) `sqrt(65) ÷ sqrt(5) = sqrt(13 xx 5)/sqrt(13) = sqrt(5)`

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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. (iv) | 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

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Can you get a pure surd when you find the product 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 =