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In this lesson, we will learn how to solve word problems about square and cube roots.

Q1:

Given that the dimensions of a rectangle are 5 7 + 7 √ 2 cm and 5 7 − 7 √ 2 cm, find the length of its perimeter.

Q2:

A cube-shaped container has a capacity of 5 1 2 𝑥 𝑦 9 2 7 . Determine the length of one of its sides.

Q3:

The radius 𝑟 of a sphere is given by the formula 𝑟 = 3 𝑉 4 𝜋 1 3 , where 𝑉 is the sphere’s volume. Determine the difference in radius between a sphere with volume 3 6 𝜋 and a sphere with 2 3 0 4 𝜋 .

Q4:

Find the volume of the cube, given that the length of its edge is 1 1 0 √ 1 2 3 cm.

Q5:

A square has a side length of 𝑙 cm and an area of 63 cm^{2}. Find the area of a square whose side length is 6 𝑙 cm.

Q6:

A modern art museum acquired a large, square painting with an area of 121 square feet. What is its side length?

Q7:

If 𝑥 = 𝑦 3 , then 𝑥 is the cube root of 𝑦 . Determine the cube root of 74 to the nearest whole number.

Q8:

In a triangle whose base and height are equal, the base length is given by 𝑏 = √ 2 𝐴 , where 𝐴 is the area of the triangle. Estimate, to the nearest whole number, the base length of this triangle if its area is 17 square meters.

Q9:

The side length, 𝑙 , of a cube is given by the formula 𝑙 = √ 𝑉 3 , where 𝑉 is the volume of the cube. What is the side length of a cube whose volume is 5 832 cm^{3}?

Q10:

Farida has 361 marbles that she will use to make a square formation. Determine the number of marbles that should be in each row.

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