10.2.1 Calculator Exploration: Square Roots

In this exploration, you will learn to use the calculator to find square roots.

Calculator IconThe calculator can be accessed on the left-hand side bar under Toolkit.

To use the calculator to find square roots, use the The button being shown is the square root key. key.

Try using your calculator to find Square root of 25.

Enter The buttons shown are the square root button, followed by the number 2, the number 5, parentheses closed, and equals sign keys.

Note that when you press the square root key, the calculator opens parentheses; you must remember to close them when you have completed the number whose square root you are finding.

Before you click the Equals key (but after you have closed the parentheses), you should see this:

Here is the completed calculation:

Activity Symbol Activity: Some Square Root Investigations

(a) Use the calculator to work out Square root of 25, Square root of 49, and Square root of open 25 plus 49 close.

Does equation left hand side Square root of 25 plus Square root of 49 equals right hand side Square root of open 25 plus 49 close?

Hint Symbol

Comment

When you enter Square root of open 25 plus 49 close, don’t close the parentheses until you have entered the whole expression under the square root sign, that is, all of 25 plus 49.

Solution Symbol

Answer

(a) Square root of 25 equals five and Square root of 49 equals seven, so equation sequence Square root of 25 plus Square root of 49 equals five plus seven equals 12.

However, equation sequence Square root of open 25 plus 49 close equals Square root of 74 equals 8.60 (to 2 decimal places).

Therefore, Square root of 25 plus Square root of 49 is not equal to Square root of open 25 plus 49 close.

So it is important to note that the square root of a sum is not the same as the sum of the individual roots.

(b) Use the calculator to work out Square root of 25, Square root of 49, and Square root of open 25 multiplication 49 close.

Does equation left hand side Square root of 25 multiplication Square root of 49 equals right hand side Square root of open 25 multiplication 49 close?

Solution Symbol

Answer

(b) Square root of 25 equals five and Square root of 49 equals seven, so equation sequence Square root of 25 multiplication Square root of 49 equals five multiplication seven equals 35.

Then, equation sequence Square root of open 25 multiplication 49 close equals Square root of 1225 equals 35.

Therefore, equation left hand side Square root of 25 multiplication Square root of 49 equals right hand side Square root of open 25 multiplication 49 close.

The square root of a product is the same as the product of the individual roots.

10.2.2 Repeating Square Roots