Question

Find the square root in the form of binomial surd:
$56-24\sqrt{5}$.

Answer 1

Square root of $56-24\sqrt{5}$

$\sqrt{56-24\sqrt{5}}=\sqrt{a}-\sqrt{b}$

squaring of both sides

$(\sqrt{56-24\sqrt{5}}{)}^2=(\sqrt{a}-\sqrt{b}{)}^2$

$56-24\sqrt{5}=a+b-2\sqrt{a\times b}$

$56-2\times 12\sqrt{5}$

$56-2\sqrt{12\times 12\times 5}$

$56-2\sqrt{6\times 2\times 6\times 2\times 5}$

$56-2\sqrt{36\times 20}$

So $-2\sqrt{ab}=-2\sqrt{36\times 20}$

So $(\sqrt{36}-\sqrt{20}{)}^2$ Ans