Respuesta :
The rationalization of all denominators is 5.74165.
A fraction is represented inside the form of 'x/y', wherein 'x' is the numerator and 'y' is the denominator. The numerator represents the entire variety of parts taken into consideration. whereas, the denominator represents the full quantity of equal components in a fraction. The pinnacle quantity in a fragment is usually taken into consideration as a numerator.
Another phrase for a denominator is the divisor. both of those words check with the range beneath the road in a not unusual fraction. similarly, while you're speakme approximately statistical values, a denominator refers back to the whole number or population from which samples are taken.
In a fallacious fraction, the numerator is extra than or the same as the denominator and the denominator must not be the same as zero. In an incorrect fraction, the numerator is less than the denominator and the numerator is extra than 0. In an unsuitable fraction, the numerator is constantly more than the denominator.
[tex]5\sqrt{2} /\sqrt{7}- \sqrt{2}[/tex]
[tex]\frac{5\sqrt{2} }{\sqrt{7}-\sqrt{2} }[/tex]
Multiply by the conjugate
[tex]\frac{5(\sqrt{7}+\sqrt{2})\sqrt{2} }{(\sqrt{7} -\sqrt{2} )(\sqrt{7} +\sqrt{2} }[/tex]
Expand [tex](\sqrt{7} -\sqrt{2} )(\sqrt{7} +\sqrt{2} ): 5[/tex]
Factor out the common term 5
[tex]\frac{(5\sqrt{7}+5 \sqrt{2})\sqrt{2} }{5}[/tex]
Cancel the common factor: 5
[tex](\sqrt{7} +\sqrt{2}) \sqrt{2}[/tex]
[tex]= \sqrt{14} +2[/tex]
= Decimal:5.74165
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