1718 WA2X §3.2

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§3.2 Square roots

What is a square root?
Finding the square root is the inverse of squaring
(In the same way that dividing is the inverse of multiplying and  subtracting is the inverse of adding)

§3.2 Square roots

Why is it called the square root?
In year 3 you will learn about the cube root, fourth root, fifth root, etc. They are the inverse of raising a number to the third power, fourth power, fifth power, etc.

§3.2 Square roots

Notation
Sometimes the square root is written as           , but           is more common.
Anything that is written under the "tail" of the square root sign should be treated as if it is written between brackets, so should be calculated before you find the square root.

§3.2 Square roots

Order of operations
1. Calculate what is between brackets
2. Raising to a power and finding roots
3. Multiply and divide from left to right
4. Add and subtract from left to right

Find the square root of 25

√​25​​​=

Find the square root of 81

√​81​​​=

Find the square root of (40+60)

√​40+60​​​=

§3.2 Square roots

Fractions and decimal numbers
You can also find the square root of fractions and decimal numbers

Find the square root of (9/100)

√​​100​​9​​​​​=

1. ​100​​4.5​​
2. ​50​​9​​
3. ​10​​3​​
4. ​20​​9​​

§3.2 Square roots

Exact answers and approximations
If you calculate some square roots, you get a whole number, a fraction or a finite decimal number:

If you calculate some square roots, you get a number with infinite decimals, that cannot be written as a fraction:
In this case, we say that        is an exact number, and we say 2.24 is an approximation accurate to two decimal places (2.236 is an approximation accurate to three decimal places, etc).

Between which two whole numbers does the square root of 30 lie?

1. 14 and 15
2. 15 and 16
3. 4 and 5
4. 5 and 6

Give an approximation of the square root of 13, accurate to two decimal places.

√​13​​​≈

Homework