Rationalize the denominators of the following:1/(√7 - √6)

1.	Rationalize the denominators of the following:1/(√7 - √6)
Answer» 1/(√7 - √6) We need to multiply the numerator and denominator of 1/(√7 - √6) by, √7 - √6, to get 1/(√7 - √6) x (√7 + √6) / (√7 + √6) = (√7 + √6) / (√7 - √6)(√7 + √6). We need to apply the formula (a - b)(a + b) = a² - b² in the denominator to get 1/(√7 - √6) = (√7 + √6) / ((√7)2 - (√6)2 = (√7 + √6) / 7 - 6 = √7 + √6 Therefore, we conclude that on rationalizing the denominator of 1/(√7 - √6),we get √7 + √6.

Answer»

1/(√7 - √6)

We need to multiply the numerator and denominator of 1/(√7 - √6) by, √7 - √6, to get

1/(√7 - √6) x (√7 + √6) / (√7 + √6)

= (√7 + √6) / (√7 - √6)(√7 + √6).

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

1/(√7 - √6) = (√7 + √6) / ((√7)2 - (√6)2

= (√7 + √6) / 7 - 6 = √7 + √6

Therefore, we conclude that on rationalizing the denominator of 1/(√7 - √6),we get √7 + √6.

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