How to explain square roots to kids

To many people, square roots fall into the category of things they learned in school which have never been of any use in adult life. However, square roots are specifically mentioned in The National Curriculum and equivalent documents, and teachers and parents have a duty to explain them to children. This is best achieved by building on the children’s familiarity with times tables, as new concepts are more easily learned when linked to existing knowledge, according to Carnegie Mellon University.

Lesson one

Explain square roots to kids by pointing out the relationship between the terms “square” and “square root.” Talk about square numbers and explain what they are. Keep to whole numbers in the first instance. Give examples of square numbers and how they are produced, for example 4 x 4 = 16, 5 x 5 = 25 and 6 x 6 = 36. Write these on the board. Ask the children what is special about square numbers. Tease out the response that they are the product of multiplying two numbers that are the same, to confirm they have understood the concept.

Ask the children for any other numbers that are the product of multiplying two numbers that are the same. Write them on the board until you have all the square numbers up to 100. Ask a child to come up to the board and add the multiplicand and multiplier for one of the other square numbers. Ask other children to do the same for the other square numbers until you have them all on the board.

Introduce the concept of square root. Refer to square root as being the opposite of square. Ask relevant questions to ensure the children understand this idea. Draw the square root symbol on the board and optionally explain it is called a radical sign, as they may well be aware of the word “rad” in other contexts. Give the children a pre-prepared worksheet on which there are square root questions for the square roots of perfect square numbers up to 100.

Lesson two

Point out that a negative number multiplied by a negative number gives a positive number, therefore all square numbers have two square roots. Demonstrate this on the board.

Discuss and give examples of square roots of numbers that are not perfect squares. The square roots of the numbers 5, 7 and 8, for example, are harder to calculate.

Give the children a prepared worksheet to test their knowledge. Cover negative square roots and the square roots of numbers that are not perfect squares.

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About the Author

Frank Luger had his first educational resources published in the early 1990s. He worked on a major reading system for Cambridge University Press, became an information-technology adviser and authored interactive whiteboard resources for "The Guardian." Luger studied English literature and holds a Bachelor of Education honors degree from Leeds University.