Real Number Quiz 11

$\sqrt[3]a+\sqrt[3]b+ \sqrt[3]c=0$ then $(a+b+c)^3 = ...........$

Rationalising factor of $\sqrt[3]{16}-\sqrt[3]4+1$ 

$\frac{l}{\sqrt{10}+\sqrt{14}+\sqrt{15}+\sqrt{21}}=\frac{\sqrt{10}-\sqrt{14}-\sqrt15+\sqrt21}{k}$ then k = …………

A rationalising factor of $\sqrt[3]{25}+\frac{1}{\sqrt[3]{25}}-1$ is ……………

$\frac{\sqrt{x^2+1}+\sqrt{x^2-1}}{\sqrt{x^2+1}-\sqrt{x^2-1}}+\frac{\sqrt{x^2+1}-\sqrt{x^2-1}}{\sqrt{x^2+1}+\sqrt{x^2-1}}=..........$

Arithmetic mean of two surds is $5+9\sqrt2$ and one of them is $1+12\sqrt2$ then second surd is …………

$\frac{1+\sqrt2}{3-2\sqrt2}=a+b\sqrt2$ then (a, b) = ……………

$x=2\sqrt2+\sqrt7$ then $\frac{1}{2}(x-\frac{1}{x})$ = …………

If the product of two irrational numbers is rational, then which of the following can be concluded ?

Which of the following is always true?