RATIONALIZING THE DENOMINATOR

Rationalize the denominator.

Problem 1 :

Solution :

Multiply both numerator and denominator by √2, we get

Hence the answer is √2/2.

Problem 2 :

Solution :

Multiply both numerator and denominator by √2, we get

Hence the answer is √2.

Problem 3 :

Solution :

Multiply both numerator and denominator by √2, we get

Hence the answer is 2√2.

Problem 4 :

Solution :

Multiply both numerator and denominator by √3, we get

Hence the answer is √3/3.

Problem 5 :

Solution :

Multiply both numerator and denominator by √3, we get

Hence the answer is √3.

Problem 6 :

Solution :

Multiply both numerator and denominator by √3, we get

Hence the answer is 4√3/3.

Problem 7 :

Solution :

Multiply both numerator and denominator by √5, we get

Hence the answer is √5/5.

Problem 8 :

Solution :

Multiply both numerator and denominator by √5, we get

Hence the answer is 3√5/5.

Problem 9 :

Solution :

Multiply both numerator and denominator by √5, we get

Hence the answer is √15/5.

Problem 10 :

Solution :

Multiply both numerator and denominator by √2, we get

Hence the answer is √20/2.

Problem 11 :

Solution :

Multiply both numerator and denominator by √3, we get

Hence the answer is √3/6.

Problem 12 :

Solution :

Multiply both numerator and denominator by √3, we get

Hence the answer is 2√6/3.