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, $\sqrt{25}$√25. This means find the square root of $25$25.

Examples

Question 1

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

Think: $12\times12=144$12×12=144

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

 

question 2

Evaluate: $\sqrt{64}$√64

Think: $8\times8=64$8×8=64

Do: $\sqrt{64}=8$√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: $\sqrt{100}-\sqrt{49}$√100−√49

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

Do:

$\sqrt{100}-\sqrt{49}$√100−√49	$=$=	$10-7$10−7
	$=$=	$3$3

 

question 4

Evaluate: $\sqrt{14+11}$√14+11

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

Do:

$\sqrt{14+11}$√14+11	$=$=	$\sqrt{25}$√25
	$=$=	$5$5

 

Worked Examples

Question 7

 

Question 8

 

Question 9