Simplifying Radicals
Simplify the following radical: √ 54.
3√ 6
In order to add radicals, which of the following must be true?
(a) The radicals must have the same index
(b) The radicals must have the same radicand
(c) The radicals must have the same number outside the radical sign
(d) Both a and b
(d) Both a and b
Generally speaking, in order to multiply radicals, which of the following must be true?
(a) The radicals must have the same index
(b) The radicals must have the same radicand
(c) The radicals must have the same number outside the radical sign
(d) Both a and b
(a) The radicals must have the same index
Remove the radical from the denominator from the following expression: √4 / √36. Reduce your answer if necessary.
1 / 3
Which of the following is the inverse of a radical sign?
(a) Index
(b) Multiplication
(c) Exponent
(d) Fraction
(c) Exponent
Simplify the following radical: √ 18.
3√ 2
Add the following radicals: 4√3 + 2√3 + 7√3.
13√3
Multiply the following radicals: √5 x √8. Simplify if necessary.
2√10
Remove the radical from the denominator from the following expression: √7 / √3.
√21 / 3
Solve the following radical equation: √(3x +10) = 2
x =-2
Simplify the following radical: 2√ 24.
4√ 6
Subtract the following radicals: 6√5 - √125.
√5
Multiply the following radicals: √x times ∛ x. Simplify if necessary by reducing the indexes.
Sixth root of x5
Remove the radical from the denominator from the following expression: √x / √y6.
√x / y3
Solve the following radical equation: √(5x + 6) - 6 = 18.
x = 114
Simplify the following radical: 3√ 63.
9√ 7
Add the following radicals: √8 + √98 + √72.
15√2
Multiply the following radicals using F.O.I.L.: (2 - √13)2. Simplify if necessary.
17 - 4√13
Remove the radical from the denominator from the following expression: 7 / 1 + √6.
-7 + 7√6 / 5
Solve the following radical equation: √(x + 4) = √(2x - 1).
x = 5
Simplify the following radical: 4∛ 27x3.
12x
Add/Subtract the following radicals: 7√18 + 2√25 - 3√72.
10 + 3√2
Multiply the following radicals using F.O.I.L.: (2√3 - 4)2. Simplify if necessary.
28 - 16√3
Remove the radical from the denominator from the following expression: √5 / 1 - √7.
√5 + √35 / -6
Solve the following radical equation: x + 1 = √(5x + 1).
x = 0, 3