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Rationalize the denominator in1/√2+√3 |
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Answer» -step explanation:Then,\frac{1}{2+ \SQRT{3} } \times \frac{2- \sqrt{3} }{2- \sqrt{3} } = \frac{2- \sqrt{3}}{(2+ \sqrt{3})(2- \sqrt{3}) } 2+ 3 1 × 2− 3 2− 3 = (2+ 3 )(2− 3 )2− 3 We KNOW that, (a+b) ( a-b) = a² - b².So, (2+√3)(2-√3) = 2² -(√3)² = 4 - 3 = 1.Then,⇒ \frac{2- \sqrt{3}}{(2+ \sqrt{3})(2- \sqrt{3}) } = \frac{2- \sqrt{3}}{1} = 2- \sqrt{3} (2+ 3 )(2− 3 )2− 3 = 12− 3 =2− 3 Hence the DENOMINATOR is rationalized. |
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