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

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

Sum

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

Example:

(a) `sqrt(125) xx sqrt(45) = sqrt(25 xx 5) xx sqrt(9 xx 5) = 5sqrt(5) xx 3sqrt(5)` = 15 × 5 = 75

(b) `sqrt(150) xx sqrt(6) = sqrt(25 xx 6) xx sqrt(6) = 5sqrt(6) xx sqrt(6)` = 5 × 6 = 30

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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. (iii) | 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 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 difference of two surds Justify answer with an example

Find the odd one out of the following.

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