Lesson 5: Square root. Percent
Lesson 5: Square Root. Percent
Square roots and percent calculations.
In this lesson we are discussing two topics: square root of a number and percent.
A square root of a number is a number that has been squared to get the number under the square root.
For example, the √4 is 2, because 2 x 2 = 4.
Watch the video lesson to see the examples and learn why we cannot take a square root of a negative number.
We have already discussed the concept of percent in our previous lessons. However, since it is a very commonly used concept, we will go over it again in more detail.
In this lesson you will learn the general formula for finding the percent of a number. You will see how to use proportions in order to calculate percent.
Together, we will go over some real life problems with percentages.
Check your understanding with Grade 8 quizzes
Key ideas: Square Root. Percent
The square root of a number is the number that multiplies by itself to give it: √49 = 7 because 7 × 7 = 49. Numbers like 49 and 144 are perfect squares. For other numbers, estimate between two perfect squares.
Percent problems: part = percent × whole. To find a percent increase or decrease, divide the change by the original amount.
Worked examples
Example 1
Find √144 and estimate √50.
- √144 = 12.
- 49 < 50 < 64, so √50 is between 7 and 8, close to 7: ≈ 7.07.
Example 2
A square garden has an area of 81 m2. How long is each side?
- √81 = 9 m
Example 3
A $64 price goes up by 25%. What is the new price?
- 25% of 64 = 16.
- 64 + 16 = $80
Example 4
30 is 40% of what number?
- 0.40 × n = 30, so n = 30 ÷ 0.40.
- 75
Common mistakes
- Thinking √50 = 25 (that is half of 50, not its square root).
- Finding the percent of the new amount instead of the original amount.
Questions students ask
Can a square root be negative?
Every positive number has a positive and a negative square root (7 and −7 for 49), but the √ symbol means the positive one.
Check your understanding
Practise with the Grade 8 quizzes. You’ll see right away if each answer is correct.