Question

Звільнитися від ірраціональності в знаменнику дробу 5+√5/4√5СРОЧНОООО​

Answer 1

$\displaystyle\bf\\\frac{5+\sqrt{5} }{4\sqrt{5} } =\frac{(\sqrt{5} )^{2}+\sqrt{5} }{4\sqrt{5} } =\frac{\sqrt{5}\cdot(\sqrt{5} +1) }{4\sqrt{5} } =\frac{\sqrt{5}+1 }{4}$

Answer 2

Simplifying an Irrational Fraction

To simplify the irrational fraction 5√5/4√5, we can start by rationalizing the denominator. This means getting rid of the radical in the denominator.

To do this, we can multiply both the numerator and the denominator by the conjugate of the denominator. The conjugate of 4√5 is -4√5.

So, the expression becomes: 5√5/4√5 * -4√5/-4√5

This simplifies to: -20√5/(-4 * 5) -20√5/-20

Finally, the simplified form is: √5

This is the simplified form of the given irrational fraction 5√5/4√5.