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siniylev [52]
2 years ago
5

The number obtained on rationalizing the denominator of 1/(√7--2) is

Mathematics
2 answers:
Studentka2010 [4]2 years ago
8 0

Given that:

1/(√7 - 2)

The denominator is (√7-2).

We know

The rationalising factor of (√a-b) is (√a+b)

Therefore, the rationalising factor of √7-2 is √7+2.

On rationalising the denominator them

⇛[1/(√7-2)]×[(√7+2)/(√7+2)]

⇛[1(√7+2)]/[(√7-2)(√7+2)]

Since, (a-b)(a+b) = a²-b²

Where, a = √7 and b = √2.

⇛[1(√7+2)]/[(√7)²-(2)²]

⇛[1(√7+2)]/[(√7*7)-(2*2)]

⇛[1(√7+2)]/[7-4]

⇛[1(√7+2)]/3

⇛(√7+2)/3

Hence, the denominator is rationalised.

<u>also</u><u> read</u><u> similar</u><u> questions</u><u>:</u>

Slav-nsk [51]2 years ago
3 0

\frac{1}{ \sqrt{7}  -(- 2)}  \\ rationalizing \:  \:  \: the \:  \:  \: denominator \:  \:  \: we \:  \:  \: have \\  =  \frac{1}{ \sqrt{7} + 2 }  \times  \frac{ \sqrt{7}  - 2}{ \sqrt{7}  - 2}  \\  =  \frac{ \sqrt{7}  - 2}{ {( \sqrt{7} )}^{2} -  {(2)}^{2}  }  \\  =  \frac{ \sqrt{7} - 2 }{7 - 4}  \\  =  \frac{ \sqrt{7}   - 2}{3}

Hope you could get an idea from here.

Doubt clarification - use comment section.

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