Question

Fill in the blank to complete the following sentence. The two roots a +sqrt b and a- sqrt b are called ______ radicals.

Answer 1

The two roots a + sqrt b and a - sqrt b are called conjugate radicals.

Solution:

Given that the two roots a + sqrt b and a - sqrt b are called ______ radicals.

Now let us write the each of the given two radicals in mathematical form.

So, first radical ⇒ a + sqrt b ⇒
`a+√(b)` [ since sqrt means square root]

Now second radical ⇒ a - sqrt b ⇒
`a-√(b)`

We have to find the relation between
`a+√(b) \text { and } a-√(b)`

Now, if observe
`a+√(b)` is conjugate of
`a-√(b) \text { as }(a+√(b))(a-√(b))=a^(2)-b`

[ where radical is eliminated]

Hence, the two roots a +sqrt b and a- sqrt b are called conjugate radicals