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Degger [83]
2 years ago
7

Rationalise the denominator of: (√3 + √2)/(√3-√2) = ?​

Mathematics
1 answer:
krok68 [10]2 years ago
8 0

Step-by-step explanation:

<h3><u>Given</u><u>:</u><u>-</u></h3>

(√3+√2)/(√3-√2)

<h3><u>To </u><u>find</u><u>:</u><u>-</u></h3>

<u>Rationalised</u><u> form</u><u> </u><u>=</u><u> </u><u>?</u>

<h3><u>Solution</u><u>:</u><u>-</u></h3>

We have,

(√3+√2)/(√3-√2)

The denominator = √3-√2

The Rationalising factor of √3-√2 is √3+√2

On Rationalising the denominator then

=>[(√3+√2)/(√3-√2)]×[(√3+√2)/(√3+√2)]

=>[(√3+√2)(√3+√2)]×[(√3-√2)(√3+√2)]

=>(√3+√2)²/[(√3-√2)(√3+√2)]

=> (√3+√2)²/[(√3)²-(√2)²]

Since (a+b)(a-b) = a²-b²

Where , a = √3 and b = √2

=> (√3+√2)²/(3-2)

=> (√3-√2)²/1

=> (√3+√2)²

=> (√3)²+2(√3)(√2)+(√2)²

Since , (a+b)² = a²+2ab+b²

Where , a = √3 and b = √2

=> 3+2√6+2

=> 5+2√6

<h3><u>Answer:-</u></h3>

The rationalised form of (√3+√2)/(√3-√2) is 3+2√6+2.

<h3><u>Used formulae:-</u></h3>

→ (a+b)² = a²+2ab+b²

→ (a-b)² = a²-2ab+b²

→ (a+b)(a-b) = a²-b²

→ The Rationalising factor of √a-√b is √a+√b

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