Question

The positive square root of $(\sqrt{48}-\sqrt{45})$ is _________.

• A. $\frac{\sqrt[4]{43}}{\sqrt{2}}(\sqrt{5}-\sqrt{3})$
• B. $\frac{\sqrt[4]{43}}{2}(\sqrt{5}-\sqrt{3})$
• C. $\frac{\sqrt{2}}{\sqrt[4]{43}}(\sqrt{5}-\sqrt{3})$
• D. $\frac{\sqrt[4]{43}}{\sqrt{2}}(\sqrt{5}+\sqrt{3})$

Answer 1

The correct option is A $\frac{\sqrt[4]{43}}{\sqrt{2}}(\sqrt{5}-\sqrt{3})$

Solving $(\sqrt{48}-\sqrt{45})$

$4\sqrt{3}-3\sqrt{5}$

$\frac{\sqrt{3}}{2}(8-2\sqrt{15})$

$\frac{\sqrt{3}}{2}(3+5-2\sqrt{15})$

$\frac{\sqrt{3}}{2}(\sqrt{3^2}+\sqrt{5^2}-2\sqrt{5}\times \sqrt{3})$

$\frac{\sqrt{3}}{2}(\sqrt{5}-\sqrt{3}{)}^2$

$NowFindingSquareRoot$

$\pm \left\{\frac{3^{\frac{1}{4}}}{\sqrt{2}}\right(\sqrt{5}-\sqrt{3}\left)\right\}$

$Soi{t}^{\prime }spositiverootis$$\frac{3^{\frac{1}{4}}}{\sqrt{2}}(\sqrt{5}-\sqrt{3})$

Correct Answer is $A$