Question

Subtracting, Dividing, Adding, and Multiplying Radicals

Answer 1

Given

`\sqrt{6+√(11)}-\sqrt{6-√(11)}\text{ \_\_\_\_\_\_\_ }3`

To compare.

Step-by-step explanation:

It is given that,

`\sqrt{6+√(11)}-\sqrt{6-√(11)}\text{ \_\_\_\_\_\_\_ }3`

Now, consider

`√(p)=\sqrt{6+√(11)}-\sqrt{6-√(11)}`

Squaring both sides implies,

`\begin{gathered} p=(\sqrt{6+√(11)}-\sqrt{6-√(11)})^2 \\ =(6+√(11))-2(\sqrt{6+√(11)})(\sqrt{6-√(11)})+(6-√(11)) \\ =12-2(\sqrt{(6+√(11))(6-√(11))}) \\ =12-2(√(36-11)) \\ =12-2(√(25)) \\ =12-2*5 \\ =12-10 \\ =2 \end{gathered}`

That impies,

`\sqrt{6+√(11)}-\sqrt{6-√(11)}=√(2)<3`