If \(\frac{{22\sqrt 2 }}{{4\sqrt 2 - \sqrt {3\, + \,\sqrt 5 }}}\)  =  \(a + \sqrt 5 b\) , with a, b > 0, then what is the value of (ab) ∶ (a + b)?

The value of \(\frac{1}{{4 - \sqrt {15} }} - \frac{1}{{\sqrt {15} - \sqrt {14} }} + \frac{1}{{\sqrt {14} - \sqrt {13} }} - \frac{1}{{\sqrt {13} - \sqrt {12} }} + \frac{1}{{\sqrt {12} - \sqrt {11} }} - \frac{1}{{\sqrt {11} - \sqrt {10} }} + \frac{1}{{\sqrt {10} - 3}} - \frac{1}{{3 - \sqrt 8 }}\)  is:

If x = \(\sqrt {1 + \frac{{\sqrt 3 }}{2}} - \sqrt {1 - \frac{{{\kern 1pt} \sqrt 3 }}{2}} \) , then the value of  \(\frac{{\sqrt 3 - x}}{{\sqrt 3 + x}}\)  (corrected to two decimal places) is:

If \(\sqrt{1+\frac{\sqrt{3}}{2}}- \sqrt{1-\frac{\sqrt{3}}{2}}= c\) , then the value of c is:

If y = 1 + √3 + √4, then the value of 2y⁴ - 8y³ - 6y² + 28y - 84 is:

If \(\frac{\sqrt{26-7\sqrt{3} } }{\sqrt{14+5\sqrt{3} } } = \frac{b+a\sqrt{3} }{11}\) , b > 0, then what is the value of  \(\sqrt{(b-a)} \)  ?

If \(\frac{\sqrt{38-5\sqrt{3} } }{\sqrt{26+7\sqrt{3} } }= \frac{a+b\sqrt{3} }{23} \) , b > 0, then the value of (b – a) is:

If \( \frac{5}{4{\sqrt 2 }} + \frac{{3 + 2\sqrt 2 }}{{3 - 2\sqrt 2 }} - \frac{{3 - 2\sqrt 2 }}{{3 + 2\sqrt 2 }} = a + b\sqrt 2 \) , then what is the value of (3a + 4b)?

The product of \(\sqrt{2}\)  and  \(\sqrt{3}\)  is:

A terminating decimal is always:

The decimal expansion of \(\frac{27}{25}\) will terminate after:

Which of the following is a rational number between \(\sqrt{5}\)  and  \(\sqrt{7}\) ?