MATH7

MATHEMATICS 7

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What’s In

Let us see if you still know how to square a number.

Multiple Choice

What is the square of 5?

• 5

• 10

• 25

Multiple Choice

What is the square of 12?

• 144

• 121

• 24

Multiple Choice

What is the square of -9?

• 18

• -81

• 81

Multiple Choice

What is the square of  $\frac{3}{5}$ ?

•  $\frac{6}{10}$  

• 8

•  $\frac{9}{25}$  

Multiple Choice

What is the square of -10

• -10

• 100

• -100

What’s New

Take a look at this unusual wall clock and answer the questions

Multiple Choice

Can you tell the time?

• Yes

• No

Multiple Choice

The hour hand is pointed at $\sqrt{100}$ .
What is the equivalent time of  $\sqrt{100}$   in the ordinary watch?

• 100

• 10

• 1

Multiple Choice

The minute hand is pointed at $\sqrt{4}$ . 

What is the equivalent time of $\sqrt{4}$ in the ordinary watch?

• 1

• 2

• 4

Multiple Choice

Can you get the exact time if the hour hand is pointing at $\sqrt{1}$ ?  $\sqrt{36}$ ?  $\sqrt{81}$ ?

• Yes

• No

Poll

Can you get the exact time if the hour hand is pointing at  $\sqrt{10}$ ?

• Yes

• No

PRINCIPAL ROOTS OF RATIONAL AND IRRATIONAL NUMBERS

Square roots may be in the form of rational numbers. However, there are irrational square roots.

Taking the square root of a number is like doing the reverse operation of squaring a number.

Did you get it?

The radicand 1, 4, 9, 16, 36, and 81 are perfect square numbers.

Take a look at the next examples of perfect square numbers:

As you can see, every non-zero real number has 2 square roots, one positive and one negative. The positive square root of positive real numbers is the principal square root of that number.

Notice also, that the square root of perfect square numbers is rational numbers. Rational numbers are numbers that can be expressed as a ratio or quotient of two integers, where the denominator is not zero.

Activity: Be Rational

Choose “rational” if the principal root of each of the following numbers is a rational number and “ irrational” if it is not . If it is rational give its principal root.

Multiple Choice

 $\sqrt{124}$  

• Rational

• Irrational

Multiple Choice

 $\sqrt{\frac{16}{25}}$  

• Rational

• Irrational

Multiple Choice

 $\sqrt{0.04}$  

• Rational

• Irrational

Multiple Choice

 $\sqrt{121}$  

• Rational

• Irrational

Multiple Choice

 $\sqrt{0.5}$  

• Rational

• Irrational

What I Have Learned

Thank you 🙂