Question

ratinalise the denominator​

Answer 1

Step-by-step explanation:

(4√3 +5√2)/(√48 +√18)

multiply (√48 - √18) in denominator and numinator

(4√3 + 5√2)(√48 -√18) / (√48 + √18)(√48 -√18)

in denominator the equation in the form (a^2)-(b^2)=(a-b)(a+b)

and √48=√(16×3)=4√3 , √18=√(9×2)=3√2

then

= { (4√3 +5√2)(4√3 +3√2) } / { [ ( √48 )^2] -

[ (√18)^2 ]

= [ (4√3)(4√3)+(4√3)(3√2)+(5√2)(4√3)+(5√2)

(3√2) ] / [ 48- 18]

= [ 16(√3)(√3)+12(√3)(√2)+20(√2)

(√3)+15(√2)(√2) ] / [ 30]

= [ 16(48)+12√6+20√6+15(4) ] / [30]

= [ 768+32√6+60] / [30]

= [828+32√6]/[30]

= [2×(414+16√6)]/[2(15)]

= (1/30)(414+16√6)