Define surds.
Irrational numbers that cannot be simplified to remove a square root or cube root.
True or false: Surds can be expressed as fractions.
FALSE
Surds are irrational and cannot be expressed as exact fractions.
Fill in the blank: The square root of 2 is a ______.
surd
What is the simplest form of a surd?
A surd expressed with no perfect square factors under the root.
True or false: The square root of 9 is a surd.
FALSE
The square root of 9 equals 3, a rational number.
What is rationalizing a surd?
The process of eliminating the surd from the denominator of a fraction.
Define conjugate in relation to surds.
The expression formed by changing the sign between two terms in a binomial.
Fill in the blank: The conjugate of (a + √b) is ______.
a - √b
What is the product of √2 and √8?
√16, which simplifies to 4.
True or false: Surds can be added directly like rational numbers.
FALSE
Surds can only be combined if they have the same radicand.
What is the sum of √3 and √3?
2√3
Define like surds.
Surds that have the same radicand and can be combined.
Fill in the blank: The difference of √5 and √5 is ______.
0
What is the value of √(a^2) when a is a positive number?
a
True or false: Surds can be multiplied by rational numbers.
TRUE
What is the square of √7?
7
Fill in the blank: The sum of √2 and √8 is ______.
√2 + 2√2 = 3√2
Define irrational number.
A number that cannot be expressed as a fraction of two integers.
What is the simplified form of √18?
3√2
True or false: The product of two surds is always a surd.
TRUE
What is the rationalized form of 1/√3?
√3/3
Fill in the blank: The difference of √12 and √3 is ______.
√12 - √3 = 3√3 - √3 = 2√3
What is the value of √(x^2 + 4) when x = 0?
2
Define perfect square.
A number that can be expressed as the square of an integer.
