Question

simplify 3/√5-√3 please give answer by step by step​

Answer 1

i think this is the answer

Answer 2

According to the data given in the above question.

We have to find the simplification of given .

Step-by-step explanation:

Given ,

$\frac{3}{ \sqrt{5 } - \sqrt{3} }$

According to the given condition we have to rationalise the denominator,

Rationalization is defined as to multiply a rational function by a clever form of one in order to eliminate radical symbols or imaginary numbers in the denominator.

STEP-1:

Multiply numerator and denominator by a radical that will get prevent of the radical in the denominator and we get a simole number .

$Radical : √5+√3$

STEP -2:

Multiply the numerator and denominator both by radical :

$\frac{3}{ \sqrt{5 } - \sqrt{3} } \times \frac{ \sqrt{5} + \sqrt{3} }{\sqrt{5} + \sqrt{3}}$

STEP-3:

Simply the equation,we get

$\frac{3 \times(\sqrt{5} + \sqrt{3} )}{ (\sqrt{5 } - \sqrt{3} ) \times (\sqrt{5} + \sqrt{3})} \: \: \: \: \: ...(1)$

STEP-4:

we know the formula or identity from a and b form:

$(a+b)(a-b) = a²-b² \: \: \: \: \: ...(2)$

According to equation (1) and (2), we get

$\frac{3 \times(\sqrt{5} + \sqrt{3} )}{ {(\sqrt{5 })^{2} }- (\sqrt{3} )^{2}}$

Squaring the terms in denominator, we get

$\frac{3 \times(\sqrt{5} + \sqrt{3} )}{ {(5) }- (3)}$

Subtract the values in denominator and multiply the terms in numerator ,we get

$\frac{3 \times\sqrt{5} + 3 \times \sqrt{3} )}{ {2}}$

or,

$\frac{3\sqrt{5} + 3 \sqrt{3} )}{ {2}} \: is \: the \: answer$

Project code #SPJ2

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