Identifying and Simplifying surds

Simplify the following surd...

• 3√2

• 2√3

• 9√2

• 3√6

Answer explanation

To simplify the surd, factor out the square root. The expression simplifies to 3√2, as 9 can be expressed as 3², leaving √2. Thus, the correct answer is 3√2.

Simplify the following surd...

• 6√2

• 2√6

• 8√2

• 4√6

Answer explanation

To simplify the surd, factor the expression under the square root. The correct choice, 2√6, arises from simplifying √(4*6) to 2√6, as 4 is a perfect square. Thus, 2√6 is the simplest form.

Simplify the following surd...

• 4√2

• 2√3

• 6√2

• 4√3

Answer explanation

To simplify the surd, factor out the perfect square. For example, √18 = √(9*2) = 3√2. If the expression simplifies to 2√3, it indicates that the original surd was likely √12, which simplifies correctly to 2√3.

Simplify the following surd...

• 5√2

• 5√3

• 2√5

• 10√5

Answer explanation

To simplify the surd, factor out the perfect square. The expression simplifies to 5√2, as 25 can be expressed as 5², leaving √2. Thus, the correct answer is 5√2.

Simplify the following surd...

• 2√2

• 4√2

• 2√4

• 3√2

Answer explanation

To simplify the surd, we can factor out the square root. The expression simplifies to 2√2, which is the correct choice. The other options do not match the simplified form.

Simplify the following surd...

• 7√2

• 3√5

• 9√3

• 3√3

Answer explanation

To simplify the surd, factor the expression to find common terms. The correct simplification leads to 3√3, as it combines the factors effectively while reducing the surd to its simplest form.

Simplify the following surd...

• 5√5

• 3√5

• 15√3

• 5√3

Answer explanation

To simplify the surd, factor out common terms. The expression simplifies to 5√3, as 5 is the coefficient and √3 remains under the root. Thus, the correct answer is 5√3.

Simplify the following surd...

• 5√5

• 3√5

• 9√3

• 5√3

Answer explanation

To simplify the surd, factor out the square root. The expression simplifies to 3√5, as 9 can be expressed as 3², leaving √5. Thus, the correct answer is 3√5.

Simplify the following surd...

• 7√7

• 3√7

• 9√7

• 7√3

Answer explanation

To simplify the surd, we can factor out the square root. The expression simplifies to 3√7, as 9 can be expressed as 3², leaving us with 3√7 as the simplest form.

Simplify the following surd...

• 6√2

• 2√18

• 2√8

• 3√8

Answer explanation

To simplify the surd, we can rewrite 2√18 as 2√(9*2) = 2*3√2 = 6√2. Thus, the correct answer is 6√2.