Rationalize the denominator.

i. ii.

iii. iv.

i. The rationalizing factor of √7 + √2 is √7 – √2. Therefore, multiply both numerator and denominator by √7 – √2.

[∵ (a-b)(a+b) = a² – b²]

ii. The rationalizing factor of 2√5 – 3√2 is 2√5 + 3√2. Therefore, multiply both numerator and denominator by 2√5 + 3√2.

[∵ (a-b)(a+b) = a² – b²]

iii. The rationalizing factor of 7 + 4√3 is 7 – 4√3. Therefore, multiply both numerator and denominator by 7 – 4√3.

[∵ (a-b)(a+b) = a² – b²]

iv. The rationalizing factor of √5 + √3 is √5 - √3. Therefore, multiply both numerator and denominator by √5 - √3.

[∵ (a-b)(a+b) = a² – b²]

[∵ (a-b)² = a² + b² – 2ab]