Question

Simplify : $(\sqrt[4]{46}-\sqrt[4]{45})(\sqrt[4]{46}+\sqrt[4]{45})(\sqrt{6}+\sqrt{5})$

• A. $1$
• B. $2$
• C. $0$
• D. $3$

Answer 1

Answer: (A)

$1$

$(\sqrt[4]{46}-\sqrt[4]{45})(\sqrt[4]{46}+\sqrt[4]{45})(\sqrt{6}+\sqrt{5})$
$=\left[\right(\sqrt[4]{46}{)}^2-\left(\sqrt[4]{45}{)}^2\right][\sqrt{6}+\sqrt{5}]$ [Since, $(a-b)(a+b)=a^2-b^2$ ]
$=[\sqrt{6}-\sqrt{5}][\sqrt{6}+\sqrt{5}]$ [Since, $\sqrt[4]{4x^2}=\sqrt[2]{2x}$]
$=[\sqrt{6}{]}^2-[\sqrt{5}{]}^2=6-5=1$