Question

the square of an integer is called a
generate the first 10 perfect squares below:
1² 2² 3² 4² 5² 6² 7² 8² 9² 10²

the opposite of squaring a number is finding the
positive numbers have square roots.

why? what number(s) can you square to get 16?

negative numbers have square roots.
what number only has one square root?
the radical sign, √x, is used to indicate the square root of x.

√x is used to indicate the square root of x.

-√x is used to indicate the square root of x.

directions: find each square root.

1. √49
2. √9
3. -√4
4. -√289
5. -√196
6. √484
7. √(1/16)
8. -√(81/25)
9. √(49/144)

directions: circle each value that is a perfect square.
9 32 50 121 1 160 64 200 324
if a number is not a perfect square, its called a non - perfect square.

Explanation:

Step1: Recall perfect - square concept

A perfect square is the square of an integer. The first 10 perfect squares are: $1^2 = 1$, $2^2=4$, $3^2 = 9$, $4^2=16$, $5^2 = 25$, $6^2=36$, $7^2 = 49$, $8^2=64$, $9^2 = 81$, $10^2=100$.

Step2: Recall square - root concept

The opposite of squaring a number is finding the square root. Positive numbers have two square roots (a positive and a negative one). For example, to get 16, we can square 4 ($4^2 = 16$) and - 4 ($(-4)^2=16$). Negative numbers have no real - square roots in the set of real numbers. The number 0 only has one square root, which is 0 itself. The symbol $\sqrt{x}$ represents the principal (positive) square root of x, and $-\sqrt{x}$ represents the negative square root of x.

Step3: Calculate square roots

1. For $\sqrt{49}$, since $7^2 = 49$, $\sqrt{49}=7$.
2. For $\sqrt{9}$, since $3^2 = 9$, $\sqrt{9}=3$.
3. For $-\sqrt{4}$, since $2^2 = 4$, $-\sqrt{4}=-2$.
4. For $-\sqrt{289}$, since $17^2 = 289$, $-\sqrt{289}=-17$.
5. For $-\sqrt{196}$, since $14^2 = 196$, $-\sqrt{196}=-14$.
6. For $\sqrt{484}$, since $22^2 = 484$, $\sqrt{484}=22$.
7. For $\sqrt{\frac{1}{16}}$, since $(\frac{1}{4})^2=\frac{1}{16}$, $\sqrt{\frac{1}{16}}=\frac{1}{4}$.
8. For $-\sqrt{\frac{81}{25}}$, since $(\frac{9}{5})^2=\frac{81}{25}$, $-\sqrt{\frac{81}{25}}=-\frac{9}{5}$.
9. For $\sqrt{\frac{49}{144}}$, since $(\frac{7}{12})^2=\frac{49}{144}$, $\sqrt{\frac{49}{144}}=\frac{7}{12}$.

Step4: Identify perfect squares

9 is a perfect square ($3^2 = 9$), 121 is a perfect square ($11^2 = 121$), 1 is a perfect square ($1^2 = 1$), 64 is a perfect square ($8^2 = 64$), 324 is a perfect square ($18^2 = 324$). 32, 50, 160, 200 are non - perfect squares.

Answer:

1. 7
2. 3
3. - 2
4. - 17
5. - 14
6. 22
7. $\frac{1}{4}$
8. $-\frac{9}{5}$
9. $\frac{7}{12}$

Perfect squares to circle: 9, 121, 1, 64, 324