Word Problems- Simplifying Irrationals

During a math club meeting, Alex presents a challenge to identify the irrational number from the following options: √25, 3.14, 1/3, √2. Which one is it?

• √2

• 1/2

• 3.14

• √25

John is working on a landscaping project and needs to calculate the total amount of material needed. He calculates that one section requires 2√18 cubic meters of soil and another section requires 3√8 cubic meters of soil. How much soil does he need in total?

• 10√2

• 5√10

• 12√2

• 4√10

John is working on a gardening project and needs to calculate the area of a square plot. The equation representing the area in terms of one side length is x^2 + 6x + 9. Help John by factoring this perfect square trinomial.

• (x + 4)^2

• (x + 2)^2

• (x + 3)^2

• (x + 5)^2

During a math competition, Alex is presented with a list of numbers and asked to identify the irrational number among them: 0.5, √16, 2/3, √5. Which one should Alex choose?

• 2/3

• √16

• √5

• 0.5

John is trying to simplify his garden's area calculation. He has two sections, one is 5 times the square root of 50 square meters, and the other is 2 times the square root of 32 square meters. How much area does he have in total after simplification?

• 10√2 - 8√2

• 10√5 - 8√2

• 3√50 - 2√32

• 5√2 - 2√8

A rectangle garden has a length of (x - 5) meters and a width of (x - 5) meters. If the area of the garden can be represented by the expression x^2 - 10x + 25 square meters, what is the correct factorization of the area?

• (x - 10)^2

• (x - 3)^2

• (x - 5)^2

• (x - 7)^2

During a math competition, Alex is presented with a list of numbers and is asked to identify the irrational number from the following: 0.25, √36, 4/5, √3

• √36

• 4/5

• 0.25

• √3

John is working on a landscaping project and needs to calculate the amount of material needed. He figures out he needs 4 times the square root of 75 cubic meters of sand and the square root of 27 cubic meters of gravel. How much of each does he need?

• 12√3 + 2√3 cubic meters

• 15√3 + 3√3 cubic meters

• 18√3 + 5√3 cubic meters

• 10√3 + 4√3 cubic meters

John is working on a gardening project and needs to calculate the area of a square plot. The equation representing the area is x^2 + 12x + 36. Help John by factoring this perfect square trinomial.

• (x + 6)^2

• (x + 12)^2

• (x + 18)^2

• (x + 24)^2

During a math competition, Alex is presented with a list of numbers and is asked to identify the irrational number from the following: 0.2, √49, 3/4, √7

• 3/4

• √7

• √49

• 0.2