Finding the square root of a number is the opposite operation to squaring a number.
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.
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
Evaluate: $\sqrt{64}$√64
Think: $8\times8=64$8×8=64
Do: $\sqrt{64}=8$√64=8
Now let's look at putting all this knowledge together in different types of questions.
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 |
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 |
Evaluate $\sqrt{25}-\sqrt{9}$√25−√9
Evaluate $\sqrt{8^2+6^2}$√82+62
Evaluate $\sqrt[3]{512}\times\sqrt[3]{64}$3√512×3√64