Question

Rationalize the denominator 1/root5 with explaination​

Answer 1

Answer:

= √5/5

Step-by-step explanation:

★ Rationalizing factor :

⇒ The factor of multiplication by which rationalization is done, is called as rationalizing factor.

⇒ If the product of two surds is a rational number, then each surd is a rationalizing factor to other.

⇒ To find the rationalizing factor,  

   =>  If the denominator contains 2 terms, just change the sign between the two terms.

       For example, rationalizing factor of (3 + √2) is (3 - √2)

  => If the denominator contains 1 term, the radical found in the denominator is the factor.

       For example, rationalizing factor of √2 is √2

_______________________

Given fraction,  $\sf \dfrac{1}{\sqrt{5}}$

Since the denominator contains only one term, the radical found in the denominator is √5. Hence, it is the rationalizing factor.

Rationalizing factor = √5

Multiply and divide the given fraction by √5 to rationalize the denominator.

   $\longrightarrow \sf \dfrac{1}{\sqrt{5}} \times \dfrac{\sqrt{5}}{\sqrt{5}} \\\\ \longrightarrow \sf \dfrac{\sqrt{5}}{(\sqrt{5})(\sqrt{5})} \\\\ \longrightarrow \sf \dfrac{\sqrt{5}}{\sqrt{5}^2} \\\\ \longrightarrow \sf \dfrac{\sqrt{5}}{5}$

Therefore, 1/√5 = √5/5