Question

nationalise the denomination 1 over under root 5
​

Answer 1

Answer:

-root5/1

Step-by-step explanation:

1 /root5

1/root5/ -root5/-root5

-root5/root5 -root5

-root5/1 Ans

Answer 2

Question :-

Rationalize the Denominator : $\dfrac{1}{\sqrt 5}$

$\begin {gathered} \end {gathered}$

Solution :-

Given,

$\dfrac{1}{\sqrt 5}$ is an Irrational Number . . .

$\begin {gathered} \end {gathered}$

On Multiplying the Numerator and the Denominator of the Given Number by $\sqrt 5$, we have -

$\bold {\dfrac{1}{\sqrt 5}} = \dfrac{1}{\sqrt 5} \times \dfrac{\sqrt 5}{\sqrt 5} = \dfrac{\sqrt 5}{(\sqrt 5)^2} = \dfrac{\sqrt 5}{(5^\frac{1}{2})^2} = \bold {\dfrac{\sqrt 5}{5}}$

Hence, the Rationalized Form of $\dfrac{1}{\sqrt 5}$ is $\bf \dfrac{\sqrt 5}{5}$ . . .

$\begin {gathered} \end {gathered}$

Laws Used :-

i. $\sqrt[n]{a} = a^\frac{1}{n}$

ii. $(a^m)^n = a^{m \times n}$

$\begin {gathered} \end {gathered}$

Additional Information :-

Rationalization :- It is the Process of converting a Number whose Denominator is Irrational, into an Equivalent Expression with a Rational Denominator.

This is done by Multiplying the Number (i.e., Both Numerator and the Denominator) by a Number which is called as the Rationalizing Factor . . .

$\begin {gathered} \end {gathered}$

Some more Laws of Exponents :-

i. $a^m \times a^n = a^{m+n}$

ii. $\dfrac{a^m}{a^n} = a^{m - n}$

iii. $a^m \times b^m = (a \times b)^m$

iv. $\Big (\dfrac{a}{b} \Big )^m = \dfrac{a^m}{b^m}$

v. $a^{-n} = \dfrac{1}{a^n}$

vi. $a^0 = 1$