## Envision Math Grade 8, Volume 1, Chapter 1: Real Number

**Page 37 Exercise 1 Answer**

Irrational numbers cannot be represented as a fraction.

Irrational numbers are non-terminating and non-repeating in nature.

Only terminating and repeating decimals can be represented as a fraction.

Rational numbers are terminating and repeating in nature.

Only rational numbers can be represented as a fraction while irrational numbers cannot.

Terminating and repeating decimals are known as rational numbers while non-repeating decimals are known as irrational numbers.

**Page 37 Exercise 3 Answer**

We need to find whether the number √8 is greater than, less than or equal to 4.

Finding where the given square root number lie in the number line, thus,

√4 < √8 < √9

2 < √8 < 3

Thus, the value of √8 is less than the number 3.

Therefore, the number √8 is less than the number 4.

The number √8 is less than the number 4.

**Page 37 Exercise 4 Answer**

We need to solve m^{2} = 14

Solving the given expression, we get,

m^{2} = 14

m = √14

m = ±√14

The solutions are m = +√14 and m = −√14

**Page 37 Exercise 6 Answer**

We need to write \(1 . \overline{12}\) as a mixed number.

Writing the given numbers as a mixed fraction, we get,

x = 1.121212…

100x = 112.121212…

100x – x = 112.121212… – 1.121212…

99x = 112 – 1

99x = 111

\(x=\frac{111}{99}\) \(x=1 \frac{12}{99}\)The number is represented as mixed fraction as \(x=1 \frac{12}{99}\)

**Page 38 Exercise 1 Answer**

Given that the table shows the results of the draw. The students who drew rational numbers will form the team called the Tigers. The students who drew irrational numbers will form the team called the Lions. We need to list the members of each team.

The students who drew rational numbers will form the team called the Tigers.

The students who drew irrational numbers will form the team called the Lions.

Lydia drawn √38

The number 38 is not a perfect square. Hence, it is an irrational number.

Marcy drawn \(6.3 \overline{4}\)

The number is repeating in nature. Hence, it is a rational number.

Caleb drawn √36

The number 36 is a perfect square. Hence, it is a rational number.

Ryan drawn 6.343443444…

The number is non terminating and non-repeating. Hence, it is an irrational number.

Anya drawn \(6 . \overline{34}\)

The number is repeating in nature. Hence, it is a rational number.

Chan drawn √34

The number 34 is not a perfect square. Hence, it is an irrational number.

Lydia – Irrational number

Marcy – Rational number

Caleb – Rational number

Ryan – Irrational number

Anya – Rational number

Chan – Irrational number

**Team Tigers:**

Marcy, Caleb, Anya

**Team Lions:**

Lydia, Ryan, Chan

**Team Tigers:**

Marcy, Caleb, Anya

**Team Lions:**

Lydia, Ryan, Chan

**Page 38 Exercise 2 Answer**

Given that the student on each team who drew the greatest number will be the captain of that team. We need to find who will be the captain of the Tigers.

The numbers drawn by the members of the team Tigers will be,

Marcy – \(6.3 \overline{4}\)

Cleb – √36

Anya – \(6 . \overline{34}\)

Thus, the numbers are,

\(6.3 \overline{4}\) = 6.344444…

√36 = 6

\(6 . \overline{34}\) = 6.343434…

The greatest number among them will be \(6.3 \overline{4}\)

Therefore, Marcy will be the captain of the Tigers.

Marcy will be the captain of the Tigers.