Question

Rationalise 4root3 + 5root2/4root3+3root2

Answer 1

Step-by-step explanation:

(4√3 +5√2)/(4√3+3√2) =(4√3 +5√2) (4√3-3√2) / (4√3+3√2) (4√3-3√2)

=(4√3)2 +4√3(5√2 -3√2 -5√2*3√2) / [(4√3)2 -3√2)2 ]

=(48+8√6 -30) / (48- 18)

=(18 + 8√6)/ 30

=(9+4√6)/ 15

Answer 2

Answer:

The answer is 9+4root6/15

Step-by-step explanation:

To rationalize 4root3 + 5root2/4root3 + 3root2

Step = multiply both the numerator and the denominator with conjugate of the denominator(4root3 + 3root2)

That is (4root3 - 3root2)[conjugate of the denominator]

So,

4root3 + 5root2 /4root3 + 3root2 X 4root3 - 3root2/4root3 - 3root2

= (4root3 + 5root2)(4root3 - 3root2)/(4root3 + 3root2)(4root3 - 3root2)

= 4root3 X 4root3 - 4root3 X 3root2 + 5root2 X 4root3 - 5root2 X 3root2(using distributive property)/(4root3)^2 - (3root2)^2(using identity a^2 - b^2 = (a + b)(a - b)

After doing multiplication the result comes

= 16 X 3 - 12root6 + 20root6 - 15 X 2/48 - 18

= 18 + 8root6/30

= 9 + 4root6/15

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