Question

Find the square root in the form of binomial surd:
$8+\sqrt{63}$.

Answer 1

Square root of $8+\sqrt{63}$

$\sqrt{8+\sqrt{63}}=\sqrt{a}+\sqrt{b}$

Squaring of both sides

$(\sqrt{8}+\sqrt{63}{)}^2=(\sqrt{a}+\sqrt{b}{)}^2$

$8+\sqrt{63}=(\sqrt{a}{)}^2+(\sqrt{b}{)}^2+2\sqrt{ab}$

$\frac{(8+\sqrt{63}\times 2)}{1\times 2}=a+b+2\sqrt{ab}$

$\frac{16+2\sqrt{63}}{2}$

$a+b=16$

$2\sqrt{ab}=2\sqrt{63}$

$=2\sqrt{9\times 7}$

$\frac{(\sqrt{9}+\sqrt{7}{)}^2}{2}$

$\frac{(3+\sqrt{7}{)}^2}{2}$ Answer