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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.


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.


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.


$\sqrt{100}-\sqrt{49}$10049 $=$= $10-7$107
  $=$= $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.


$\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




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

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