Question

Rationalise the denominator : 5√7/√3

Answer 1

Answer:

5 / (√7+√2)

Your problem has two terms in the denominator: a + b

(a + b)(a - b) = a² - b²

(√7 + √2) * (√7 - √2)

= (√7)² - (√2)²

= 7 - 2

= 5

Therefore,

= [original fraction] * (√7 - √2) / (√7 - √2)

= [5 / (√7 + √2)] * [(√7 - √2) / (√7 - √2)]

Multiply both numerators and multiply both denominators, just as you would when multiplying any two fractions:

= [5 * (√7 - √2)] / [(√7 + √2) * (√7 - √2)]

= [5 * (√7 - √2)] / [(√7)² - (√2)²]

= [5 * (√7 - √2)] / (7 - 2)

= [5 * (√7 - √2)] / (5)

= [5 * (√7 - √2)] / 5

= (√7 - √2) * (5 / 5)

= (√7 - √2) * (1)

= (√7 - √2)

= √7 - √2

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