Question

Rationalise the denominators of the following: (b) 2√7+1/√7

Answer 1

Answer:

$\underline { \boxed{\sf { \dfrac{14+ \sqrt{7} }{7} }}} \; \bigstar$

Step-by-step explanation:

To rationalise the denominator of :

$\implies \sf { \dfrac{2\sqrt{7} + 1}{\sqrt{7} }}$

Clarification :

Before commencing the steps, let's understand how to rationalise the denominator.

In order to rationalise the denominator of the fraction, we multiply the rationalising factor of the denominator with the numerator and the denominator of the given fraction.

Rationalising factor of √a is √a. This is because, when √a is multiplied with √a, it becomes a which is rational. So, the rationalising factor of √7 is √7.

Explication of steps :

$\implies \sf { \dfrac{2\sqrt{7} + 1}{\sqrt{7} } }$

$\implies \sf { \dfrac{2\sqrt{7} + 1}{\sqrt{7}} \times \dfrac{\sqrt{7}}{\sqrt{7}} }$

$\implies \sf { \dfrac{\sqrt{7}(2\sqrt{7} + 1)}{(\sqrt{7})^2} }$

$\implies \sf { \dfrac{\sqrt{7}(2\sqrt{7} )+ \sqrt{7}(1)}{(\sqrt{7})^2} }$

$\implies \sf { \dfrac{(2\times \sqrt{7} \times\sqrt{7} )+ \sqrt{7} }{7} }$

$\implies \sf { \dfrac{(2\times 7 )+ \sqrt{7} }{7} }$

$\implies \underline { \boxed{\sf { \dfrac{14+ \sqrt{7} }{7} }}} \; \bigstar$

Hence, rationalised.

Some related identities of indices :

• (√a)² = a

• √a√b = √ab

• √a/√b = √a/b

• (√a + √b)(√a - √b) = a - b

• (a + √b)(a - √b) = a² - b

• (√a ± √b)² = a ± 2√ab + b

• (√a + √b)(√c + √d) = √ac + √ad + √bc + √bd