Square Roots

Finding the square root of a number is the opposite operation to squaring a number. 

Finding the square root

If we are asked to find the square root of a value, we are being asked, "What number multiplied by itself would give this value?"

You might also see the square root symbol written with a number inside it. For example, $$√25. This means find the square root of $$25.

Examples

Question 1

Evaluate: What is the square root of $$144?

Think: $$12×12=144

Do: The square root of $$144 is $$12

 

question 2

Evaluate: $$√64

Think: $$8×8=64

Do: $$√64=8 

 

 

Solving problems with square roots 

Now let's look at putting all this knowledge together in different types of questions.

Examples

question 3

Evaluate: $$√100−√49

Think: The square root of $$100 is $$10 and the square root of $$49 is $$7.

Do:

$$√100−√49	$$=	$$10−7
	$$=	$$3

 

question 4

Evaluate: $$√14+11

Think: Since $$14+11 is all under the square root, it is like it is in imaginary brackets and you solve this first.

Do:

$$√14+11	$$=	$$√25
	$$=	$$5

 

Worked Examples

Question 7

 

Question 8

 

Question 9