Question

x^2=49/20 is irrational number if yes how

Answer 1

x² = 49 / 20

x = 7 / 2√5  = 0.7 √5
√5 cannot be expressed as a rational number.  so x is an irrational number.

another way.
y² - 5 = 0            Rational roots if any could be : +- factors of 5 / +-1
                                                 =  +- 5
Since y is not equal to +- 5, It implies that no rational roots exist for y² - 5 =0
So y is irrational.    So √5 is irrational.

Answer 2

$x^2=\frac{49}{20}\\\\x=\pm\sqrt\frac{49}{20}\\\\x=\pm\frac{\sqrt{49}}{\sqrt{20}}\\\\x=\pm\frac{7}{\sqrt{4\cdot5}}\\\\x=\pm\frac{7}{2\sqrt5}\cdot\frac{\sqrt5}{\sqrt5}\\\\x=\pm\frac{7\sqrt5}{2\cdot5}\\\\x=\pm\frac{7\sqrt5}{10}-irrational\ number\ because\ \sqrt5\ is\ irrational\ number$