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SQUARE ROOT AND CUBE ROOT OF NUMBERS

In these worksheets, grade 7 and grade 8 students will find the square root and cube root of numbers. The previous topic was to find the squares and cubes of numbers. If you haven’t practiced them use the following link to download the worksheets for free.

https://www.mathfunworksheets.com/squares-and-cubes-of-numbers/

Now, let’s find the relationship between the squares and square root of numbers and cubes and cube root of numbers. To begin with a simple example, the square of 2 is 4 and the square root of 4 is 2. Similarly the cube of 3 is 9 and the cube root of 9 is 3. So, we conclude the square root and cube root are the opposite of squares and cubes of numbers.

How do you denote the square root and cube root? We use special symbols. Square root is denoted by ‘√’ and cube root by ‘ ∛’. Thus √64 = 8 and ∛125 = 5.

To find the square root and cube root of large numbers, we have to use prime factorization method.  An example is shown below:

  1. Find the square root of 144.

Prime factorization of 144 = 2 x 2 x 2 x 2 x 3 x 3

                                           = (22  x 2x 32)

                                           = (2 x 2 x 3) 2

Taking square root on both sides

                                  √144 = 12

  1. Find the cube root of 2744.

Prime factorization of 2744 = 2 x 2 x 2 x 7 x 7 x 7

                                            = (23  x 73 )

                                            = (2 x 7) 3

Taking cube root on both sides

                                  ∛2744 = 14

To find the square root and cube root of very large numbers and imperfect squares and cubes, we have to use long division method.

square root and cube root square root and cube root

These are the easiest methods to find the square root and cube root of numbers. Download all the worksheets to practice. Understand, this is an important concept to solve other math.

SQUARE ROOT AND CUBE ROOT- DOWNLOAD PDF SHEETS

Square root - Fractions and Decimals

Cube root - Decimals & Fractions

Finding roots - Long Division method

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