Question

Find the square root in the form of binomial surd:
$6+\sqrt{35}$.

Answer 1

Square root of

$6+\sqrt{35}$

$\sqrt{6+\sqrt{35}}=\sqrt{a}+\sqrt{b}$

Squaring of both sides

$(\sqrt{6+\sqrt{35}}{)}^2=(\sqrt{a}+\sqrt{b}{)}^2$

$6+\sqrt{35}=a+b+2\sqrt{ab}$

$\frac{(6+\sqrt{35})\times 2}{1\times 2}$

$\frac{12+2\sqrt{35}}{2}$

$\therefore a+b=12$

$2\sqrt{ab}=2\sqrt{35}$

$=2\sqrt{7\times 5}$

So $\frac{(\sqrt{7}+\sqrt{5}{)}^2}{2}$ Answer