Question

The number $\sqrt{18+\sqrt{308}}$ can be written in the form $\sqrt{a}+\sqrt{b}$ where a and b are whole numbers and a > b. The value of $(a-b)$ is:

• A. 4
• B. 12
• C. 16
• D. 18

Answer 1

The correct option is A 4

We have,

$\sqrt{18+\sqrt{308}}=\sqrt{a}+\sqrt{b}$

On squaring both sides, we get

$(\sqrt{18+\sqrt{308}}{)}^2=(\sqrt{a}+\sqrt{b}{)}^2$

$18+\sqrt{308}=(a+b)+2\sqrt{ab}$

$18+2\sqrt{77}=(a+b)+2\sqrt{ab}$

On comparing both sides, we get

$a+b=18$

$ab=77$

Since,

$(a-b{)}^2=(a+b{)}^2-4ab$

Therefore,

$(a-b{)}^2=(18{)}^2-4\times 77$

$(a-b{)}^2=324-308$

$(a-b{)}^2=16$

$a-b=4$

Hence, this is the answer.