Is finding the square root the same as squaring a number?
This is a question that I get ALL the time from my students! So firstly, let’s clarify this:
No, they are not the same in fact they are the opposite of each other!
What is the difference between a square number and a square root?
Square Numbers are the product of a number multiplied by itself.
Square Root is the base number that was multiplied by itself to make a square number.
Hands on activity to introduce Square Numbers
Provide each student (or group of students) with a packet of counters, they need to make three different sized squares using the counters. Once students have finished creating get students to discuss the following questions:
- How many counters did you use in each square? (25)
- What is the length and width, using counters as the measurement? (5)
- Could you make a perfect square using 2 less counters? (No)
Lead these questions into conversations about what makes a square number and how to discover if a number is a square number (is it the product of the same number being multiplied together?).
This activity works great to visually explain the concept of square numbers and their roots and perfect to refer to throughout your unit.
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Perfect and Imperfect Square Numbers
So far we have identified how to identify PERFECT square numbers. But only a few numbers are ‘perfect squares. The rest can be classified as IMPERFECT SQUARES.
Imperfect squares are numbers whose square roots contain fractions or decimals (are not whole numbers).
Hands on Activity to Introduce Imperfect Square Numbers
Sorting activities are a great way for students to classify perfect and imperfect square numbers. I write a whole lot of numbers on small pieces of paper (Post-It notes are brilliant!) and students sort them into to labelled columns – Perfect and Imperfect. A great differentiation tool would be to provide a multiplication chart to help students identify products.
This can be done as a partner activity, small groups or whole class!
Don’t have time to cut out heaps of little pieces of paper??
Easy, just write the numbers on the board and get students to write them down into the two columns! Also remember that these are perfect activities to display on a learning wall for students to refer to throughout the unit of study!
This sorting activity is included in the PowerPoint square number lesson plan that you can purchase from my TPT store here!
Approximating imperfect square roots
Finding the square roots of imperfect squares can be really tricky without a calculator! But, when we know our square numbers it is quite easy …. And fun to approximate!
We know that 76 is an imperfect square number because no two numbers multiplied together equal 76. Following the below steps we can approximate its square root – remembering it will NOT be a whole number!
STEPS TO FIND THE SQAURE ROOT OF AN IMPERFECT SQUARE NUMBER
STEP 1 – Identify the square numbers either side of 76.
STEP 2 – Determine the square roots of the identified numbers
STEP 3 – Position 76 on a number line between the two square numbers. Its placement corresponds with the decimal place between the squared roots.
Check on your calculator to see how close your approximation is!!!
