Rationalize the denominators of the following:1 / (√7 - 2)

1.	Rationalize the denominators of the following:1 / (√7 - 2)
Answer» 1/(√7 - 2) We need to multiply the numerator and denominator of 1/(√7 - 2) by √7 + 2, to get 1/(√7 - 2) x (√7 + 2)/(√7 + 2) = (√7 + 2)/(√7 - 2)(√7 + 2) We need to apply the formula (a - b)(a + b) = a²- b² in the denominator to get 1/(√7 - 2) = (√7 + 2)/(√7)² - (2)² = (√7 + 2)/(7 -4) = (√7 + 2)/3 Therefore, we conclude that on rationalizing the denominator of 1/(√7 - 2), we get (√7 + 2)/3.

Answer»

1/(√7 - 2)

We need to multiply the numerator and denominator of 1/(√7 - 2) by √7 + 2, to get

1/(√7 - 2) x (√7 + 2)/(√7 + 2)

= (√7 + 2)/(√7 - 2)(√7 + 2)

We need to apply the formula (a - b)(a + b) = a²- b² in the denominator to get

1/(√7 - 2) = (√7 + 2)/(√7)² - (2)²

= (√7 + 2)/(7 -4)

= (√7 + 2)/3

Therefore, we conclude that on rationalizing the denominator of 1/(√7 - 2), we get (√7 + 2)/3.

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