# Square Root Word Problems Worksheets

If we remember back, a square root is a factor of a value that when it is multiplied by itself gives you the original value. This form of math is usually stated with the symbol (√ ). We can illustrate this concept by accepting that 5 x 5 = 25. With this in mind, that would mean that the square root of 25 is 5 or √25 = 5. While this type of math just feels like a fun puzzle solving activity, there are a great many uses for square roots in the real world such as architecture, engineering, and even farming. Not to mention that it is a key aspect of solving any problem that includes a right triangle to find a measure of a missing side or angle through Pythagorean Theorem. These worksheets and lessons provide practice word problems that require the use of a square root at some point in the process.

### Aligned Standard: Grade 8 Expressions and Equations - 8.EE.A.2

- Mr. Mason's Tile Project Lesson- He knows the square footage, but how long is a side of the room he is working on?
- Application Word Problems - How much fencing does Mark need for his backyard?
- Estimation Practice Worksheet 1- Three different scenarios each with application problems.
- Exact Practice Worksheet 1 - Buying a new rug, hanging a picture, and fencing a yard.

- Answer Keys - These are for all the unlocked materials above.

### Estimating Square Roots Word Problems

You will need to round through out these problems.

- Sheet 2 - Lucy has a square table that has an area of 1.4 square meters. She buys a table cloth with an area of 2.4 square meters. How many centimeters does the cloth hang over the table on each side if put centered?
- Sheet 3 - Tim wants to put shutters on his square window. The window has an area of 1625 square inches. How high are the shutters if they are square and have an area of 2480 square inches?
- Sheet 4 - The surface of a square swimming pool has an area of 51 square yards. Around the pool there is a paved way that is 0.5 yards wide. What is the length of each side of the pool?

### Exact Square Root Word Problems

We covered just about every scenario we have ever seen on national exams with these problems.

- Sheet 2 - Sally has a bag with cubes. 9 of them are red and 16 are blue. If she makes a square that consists of all the bricks, how many bricks would be on each side?
- Sheet 3 - Carry has 169 flower seedlings and wants to plant them into a square bed. If she puts only 13 seedlings in a row but bought 196, can the remaining seedlings be used to form another square bed? How many seedlings would be on a row of this bed?
- Sheet 4 - In a town, a new big playground is built on a square area of 400 square yards. It will be divided into four equal square zones for different age groups. How many modules can be put in a row on one side of one zone without surpassing it?

### What is Square Footage?

If someone asks your age, you say "I'm 13 years old." Is that a correct use of units? You use "years old" to imply that you are thirteen years of age. Just like that, when we are talking about a large surface area, we denote these units by saying "This flat is 700 square feet."

Take your room for example. It covers up a large space in your house. The space it covers is known as surface area. Now when you measure the surface area, you will calculate it in the unit of square feet. Just like for measuring time use seconds or minutes, for surface area, the S.I unit is known as square feet. We calculate the surface areas of various shapes such as triangles, squares, rectangles and many more!

When you begin working on, just about, any construction and building project you will need to determine this measure of each room or area you are working on to determine the amount of material that you will need to complete the project. This measure also helps you determine the price of the cost of materials. Most contractors who build rooms or homes charge by this measure too. That is why tis measure warranted such a long discussion. The square footage of anything is simply the product of two measures within it: length (the longest side) and width (other side). Just multiply those values to determine the square footage.