Mastering Surds and Radicals

Simplify √50.

• √25

• 5√2

• 5√5

• 10

Rationalize the denominator of 1/√3.

• √3 / 2

• 1/3

• √3

• √3 / 3

Solve the equation √(x + 5) = 3.

• -1

• 2

• 6

• 4

What is the value of √(16) + √(9)?

• 7

• 4

• 5

• 10

Simplify √(72) - √(8).

• 8

• 2√3

• 6√2

• 4√2

Rationalize the denominator of 2/(√5 + 1).

• (2√5 + 1) / 5

• (√5 - 1) / 2

• (√5 + 1) / 2

• (√5 - 2) / 2

If √x = 7, what is the value of x?

• 49

• 25

• 56

• 14

Show that √(a) + √(b) = √(c) implies a + b = c when a, b, c are perfect squares.

• √(a) + √(b) = √(c) is always true

• √(a) + √(b) = √(c) implies a = b = c

• a + b = c when a, b, c are perfect squares.

• a + b = 2c when a, b, c are perfect squares

Simplify √(18) * √(2).

• 4

• 10

• 8

• 6

Rationalize the denominator of 3/(√2 - 1).

• 3√2 - 3

• 3√2 + 3

• 3/√2 + 1

• 3(√2 - 1)