Rationalize the denominator of 4√3+3√2/√48+√18

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Solution

4√3+3√2/√48+√18
take the LCM of √48 and √18 and take the square out

4√3+3√2/√16×3+√9×2

(4√3+3√2) / (4√3+3√2)

(4√3+3√2) (4√3- 3√2)/ (4√3+3√2)(4√3 - 3√2)

(16×3 - 12√6 +12√6 - 9×2) / (4√3)² - (3√2)²

(48 -18) / 48 - 18

20/20=1

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