Question

please give answer my friends ​

Answer 1

Answer:

kuch step kha gaya multiply divide karne vale.

Answer 2

❒ Given to Rationalize :-

$\cfrac{1}{4 \sqrt{3} - 3 \sqrt{5} }$

❒ Concept to know :-

• For rationalizing the denominator means we have to remove radicals or roots For that we have multiply and divide with its Rationalizing factor .Rationalizing factor is nothing but Conjugate for the denominator Hence in denominator (a+b)(a-b) will be formed then we can solve

❒ SOLUTION

Rationalizing factor for ,

$4 \sqrt{3} - 3 \sqrt{5} \: \: is \: \: 4 \sqrt{3} + 3 \sqrt{5}$

So, multiply and divide with this

$\dfrac{1}{4 \sqrt{3} - 3 \sqrt{5} } \times \dfrac{4 \sqrt{3} + 3 \sqrt{5} }{4 \sqrt{3} + 3 \sqrt{5} }$

$\dfrac{4 \sqrt{3} + 3 \sqrt{5} }{(4 \sqrt{3} - 3 \sqrt{5} )(4 \sqrt{3} + 3 \sqrt{5} ) }$

$\dfrac{4 \sqrt{3} + 3 \sqrt{5} }{(4 \sqrt{3} ) {}^{2} - (3 \sqrt{5}) {}^{2} }$

$\dfrac{4 \sqrt{3} + 3 \sqrt{5} }{48 - 45}$

$\dfrac{4 \sqrt{3} + 3 \sqrt{5} }{3}$

Hence denomiantor rationalized that means we can see radicals or roots removed

❒Know more:-

Algebraic Identities:-

(a+ b)² = a² + b² + 2ab

( a - b )² = a² + b² - 2ab

( a + b )² + ( a - b)² = 2a² + 2b²

( a + b )² - ( a - b)² = 4ab

( a + b + c )² = a² + b² + c² + 2ab + 2bc + 2ca

a² + b² = ( a + b)² - 2ab

(a + b )³ = a³ + b³ + 3ab ( a + b)

( a - b)³ = a³ - b³ - 3ab ( a - b)

If a + b + c = 0 then a³ + b³ + c³ = 3abc