Question

show that the sum and product of two irrational numbers 5 + root 3 and 5 minus root 3 rational numbers

Answer 1

Hey mate !!

Here's the answer !!

Refer to the attachment !!

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Answer 2

Answer:

The given two numbers are $5+\sqrt{3}$ and $5-\sqrt{3}$.

First, we have to show that the sum of these two irrational numbers will be a rational number.

Adding these two numbers we will get -

$=5+\sqrt{3}+5-\sqrt{3}\\ \\= 10$

And we know that 10 is a rational number.

Hence shows that sum of these two irrational numbers will be a rational number.

For the next part, we have to show that the product of these two irrational numbers will be a rational number.

Multiplying the numbers -

$=(5+\sqrt{3})(5-\sqrt{3})\\ \\ = 25+5\sqrt{3}-5\sqrt{3} -3\\ \\=22$

And we know that 22 is a rational number.

Hence shows that the product of these two irrational numbers will be a rational number.

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