Question

simplify 4/√7+√3

$simpify \\ 4 \div \sqrt{7} + \sqrt{3}$
​

Answer 1

Step-by-step explanation:

=4(√7-√3) divided by (√7+√3)(√7-√3)

=4(√7-√3) divided by{(√7)-(√3)}

=4(√7-√3) divided by 4

=4(√7-√3) divided by (7-3)

=4(√7-√3)× 1/4

=(√7-√3)

Answer 2

Concept Used :-

Method of Rationalization :-

• Rationalization is the process of eliminating a radical or from the denominator or numerator of an algebraic fraction. That is, remove the radicals in a fraction so that the denominator or numerator only contains a rational number.

• Rationalisation : It is the process by which the square root term or any complicated term in the denominator of a fraction is reduced by multiplying the numerator and denominator of the fraction by the same term as denominator but opposite in sign.

Let's solve the problem now!!

$\rm :\longmapsto\:\dfrac{4}{ \sqrt{7} + \sqrt{3} }$

On rationalizing the denominator, we get

$\rm :\longmapsto\: \: = \: \: \dfrac{4}{ \sqrt{7} + \sqrt{3} } \times \dfrac{ \sqrt{7} - \sqrt{3} }{ \sqrt{7} - \sqrt{3} }$

$\rm :\longmapsto\: \: = \: \:\dfrac{4( \sqrt{7} - \sqrt{3})}{ {( \sqrt{7} )}^{2} - {( \sqrt{3} )}^{2} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \red{ \because \bf \: (x + y)(x - y) = {x}^{2} - {y}^{2} }}$

$\rm :\longmapsto\: \: = \: \:\dfrac{4( \sqrt{7} - \sqrt{3)} }{7 - 3}$

$\rm :\longmapsto\: \: = \: \:\dfrac{ \cancel4( \sqrt{7} - \sqrt{3)} }{ \cancel4}$

$\rm :\longmapsto\: \: = \: \: \sqrt{7} - \sqrt{3}$

Additional Information :-

More Identities to know:

• (a + b)² = a² + 2ab + b²

• (a - b)² = a² - 2ab + b²

• a² - b² = (a + b)(a - b)

• (a + b)² = (a - b)² + 4ab

• (a - b)² = (a + b)² - 4ab

• (a + b)² + (a - b)² = 2(a² + b²)

• (a + b)³ = a³ + b³ + 3ab(a + b)

• (a - b)³ = a³ - b³ - 3ab(a - b)