Rational v Irrational
This is the type of number for sqrt(49).
What is a rational number?
The sum of two rational numbers is always this type of number.
What is a rational number?
This is the simplest radical form 4√2 + 5√2.
What is 9√2?
Daily Double:
A square garden has a side length of √16 meters. What is its perimeter?
What is 16m?
A landscaper is building a rectangular garden. The length is 4 + √5 meters and the width is 4 − √5 meters. Without multiplying directly, predict whether the area will be rational or irrational, and explain why.
What is rational — because when you multiply the length and width, the radicals cancel out: leaving a rational result 11?
The number pi or sqrt(20) is an example of this type of number.
What is an irrational number?
Daily Double:
If a is rational and b is irrational, their sum, a+b, is always this.
What is irrational?
This is the simplified form of the expression 3sqrt(5) + 2sqrt(5).
What is 5sqrt(5)?
A rectangular patio has a width of 4 m and a length of √18 m. The area and its classification is.
What is 12√2, Irrational?
The side of a square is √12 m. A second square has a side length that is double that of the first. Compare their areas and explain whether both are rational or irrational.
What is 12m2 and 48m2: rational?
The number 7sqrt(6) is this type of number because of the non-perfect square under the radical.
What is an irrational number?
If a = 2√7 and b = 4, what type of number is a × b?
What is an irrational number?
To simplify 5sqrt(18), you first break sqrt(18) into sqrt(9) * sqrt(2), resulting in this final simplified form.
What is 15sqrt(2)?
A picture frame has side lengths of 5 + √2 inches and 5 − √2 inches. What is its perimeter?
What is 20 inches?
Daily Double:
Two students simplify √18 + 2√8. Student A says it equals 5√2, while Student B says 7√2. Determine who is correct and explain the reasoning.
What is Student B: Student B is correct. √18 = 2√2 → 3√2+2(2√2) = 3√2+4√2 = 7√2 ?
Daily Double:
The decimal 4.727272... is not this type of number, as it is a repeating decimal and can be expressed as a fraction.
What is an irrational number?
Simplify and classify: 2√12 + 3√3.
What is 7√3 → Irrational ?
This is the simplified result of the product sqrt(8)*sqrt(2).
What is 4?
A landscaper designs a walkway shaped like a rectangle with length √50 ft and width √2 ft. What is the area, simplified? Rational or irrational?
What is 10 ft² (Rational)?
A homeowner is tiling a square patio with area 98 m². They decide to use square tiles with side length √2 m. Determine how many tiles will fit across one side of the patio.
What is 7√2?
An irrational number is a number that cannot be written as this type of mathematical expression.
What is a fraction of two integers (or ratio)?
Simplify: (4 + √3)(4 − √3).
What is 13?
Daily Double:
This is the simplified result of the sum 2sqrt(12) + 5sqrt(3).
What is 9sqrt(3)?
A swimming pool has sides of 6 + 2√3 m and 6 − 2√3 m. Find the area and determine if it’s rational or irrational.
What is 24 m² (Rational)?
A student claims that since √2 and √3 are both irrational, their product (√2 × √3) must also be irrational. Critique this claim using examples and reasoning.
What is the claim is not always true. √2×√3=√6√2 × √3 = √6√2×√3=√6 (irrational), but √2×√2=2√2 × √2 = 2√2×√2=2 (rational). Whether a product of irrationals is rational depends on if the radicands create a perfect square?