# Square Roots

Lesson

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}$10049

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

Evaluate $\sqrt{25}-\sqrt{9}$259

##### Question 8

Evaluate $\sqrt{8^2+6^2}$82+62

##### Question 9

Evaluate $\sqrt[3]{512}\times\sqrt[3]{64}$3512×364

### Outcomes

#### NA5-2

Use prime numbers, common factors and multiples, and powers (including square roots)