The value of an irrational number by representing it on the number line.

The video tutorial explains how to represent an irrational number, specifically the square root of 7, on a number line using three steps. First, draw and divide the number line into equal units. Second, construct a vertical line from the origin with a length of 3 units. Third, use a compass to draw an arc intersecting the number line at approximately 2.6 units, the approximate value of the square root of 7. The tutorial also introduces formulas to generalize this method for any irrational number, using a right-angle triangle approach.

What is the first step in representing the square root of 7 on the number line?

• Draw the number line and divide it into equal units.

• Draw a vertical line from the origin.

• Calculate the approximate value using a calculator.

• Use a compass to draw an arc.

In the second step, what is the length of the vertical line drawn from the origin?

• 3 units

• 7 units

• 2.6 units

• 4 units

What is the approximate value of the square root of 7 obtained in the third step?

• 3.5 units

• 2.6 units

• 5.1 units

• 4.2 units

What geometric shape is formed during the process of representing an irrational number?

• A square

• A right-angle triangle

• A rectangle

• A circle

How can the length of the hypotenuse be calculated when finding the square root of any irrational number?

• B divided by 2

• B plus 1 over 2

• B minus 1 over 2

• B times 2