Q:

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

Accepted Solution

A:
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 β‡’ a + sqrt b β‡’ [tex]a+\sqrt{b}[/tex] Β  [ since sqrt means square root]Now second radical β‡’ a - sqrt b β‡’ [tex]a-\sqrt{b}[/tex]We have to find the relation between [tex]a+\sqrt{b} \text { and } a-\sqrt{b}[/tex]Now, if observe [tex]a+\sqrt{b}[/tex] Β is conjugate of [tex]a-\sqrt{b} \text { as }(a+\sqrt{b})(a-\sqrt{b})=a^{2}-b[/tex][ where radical is eliminated]Hence, the two roots a +sqrt b and a- sqrt b are called conjugate radicals