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 ⇒ $a+\sqrt{b}$   [ since sqrt means square root]

Now second radical ⇒ a - sqrt b ⇒ $a-\sqrt{b}$

We have to find the relation between $a+\sqrt{b} \text { and } a-\sqrt{b}$

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

[ where radical is eliminated]

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