Question

simplify 3root2-2root3/3root2+2root3 +root12/root3-root2

Answer 1

Given,

3√2-2√3 /3√2 +2√3 + √12/√3-√2

Calculation,

Multiply the numerator and denominator by 3√2 - 2√3

=(3√2 -2√3)×(3√2-2√3) /(3√2 +2√3)×(3√2-2√3) + √2² ×3 /√3-√2

Using (a-b)×(a+b)=a²-b².We get,

=(3√2-2√3)×(3√2-2√3)/9×2-4×3 +√2²×√3/√3-√2

=(3√2-2√3)×(3√2-2√3)/18-12 +2√3/√3-√2

=(3√2-2√3)²/6 +2√3×(√3+√2)/(√3-√2)×(√3+√2)

Using a²-b²=(a+b)×(a-b)

=(3√2-2√3)²/6 +2√3×(√3+√2)/(√3)²-(√2)²

=(3√2-2√3)²/6 +2√3×(√3+√2)/3-2

=(3√2-2√3)²/6 +2√3×(√3+√2)/1

Using (a-b)²=a²-2ab+b²,

=(3√2)²-2×3√2×2√3+(2√3)²/6 +(2√3×√3+2√3×√2)

=9×2-12√6+4×3/6+(6+2√6)

=18-12√6+12/6 +(6+2√6)

=30-12√6/6 +(6+2√6)

=30-12√6/6+6+2√6

=6(5-2√6)/6+6+2√6

=5-2√6+6+2√6

=11

Answer=>11

Hope it helps
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