NZ Level 5

Square Roots

Lesson

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

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