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Which number is rational? (1 point)

Responses

2√4
the fraction with numerator square root of 2 and denominator 4

15−−√
square root of 15

0.23242526...
0.23242526...

0.98989898...

Which number line shows the approximate location of 48−−√
?(1 point)
Responses

Match each point with the approximation of the irrational number given.

(4 points)
Point C
Point L
Point E
Point A
responses
3V--- 1100
n
V--20
1.3242526

Order the numbers from greatest to least - use the number line to help you visualize correct placement:

Largest number first

Smallest number last

(6 points)
7/3
0
3V---27
V--15
-0.0123456
-V--45

Fill in the blanks.(6 points)
If I wanted to estimate 59−−√, the first step would be to find the two (Response area) squares that 59 lies (Response area) on the number line. The closest perfect square less than 59 is (Response area). The closest perfect square greater than 59 is (Response area). I could then think about the number 59 and how close it is to the smaller perfect square and the larger perfect square. I could then take the (Response area) root of the perfect squares to see how I would estimate 59−−√. The 59−−√ is closest to (response area)

responses
cube
perfect
9
49
6
between
square
8
7
non-perfect
64

1 answer

Let's break down each part of your questions:

  1. Which number is rational?

    • 2√4: Rational (because it equals 4).
    • The fraction with numerator square root of 2 and denominator 4: Irrational (because square root of 2 is irrational).
    • 15−−√: Irrational (because it’s a square root of a non-perfect square).
    • 0.23242526...: This is an irrational number (it doesn't terminate or repeat).
    • 0.98989898...: Rational (it is a repeating decimal, which can be expressed as a fraction).

    The rational number is: 2√4 or 0.98989898...

  2. Which number line shows the approximate location of √48?

    • √48 ≈ 6.928 (between √36=6 and √49=7).
    • Therefore, you'd be looking for a point on the number line between points representing 6 and 7.

  3. Order the numbers from greatest to least: \(7/3\), 0, \(3\sqrt{27}\), \( \sqrt{15} \), -0.0123456, -\( \sqrt{45} \)

    • First, calculate:
      • \(3\sqrt{27} \approx 3 \cdot 5.196 = 15.588\)
      • \(-\sqrt{45} \approx -6.708\)
      • \(\frac{7}{3} \approx 2.333\)
      • \(\sqrt{15} \approx 3.873\)

    So we have:

    • \(3\sqrt{27} \approx 15.588\) (greatest)
    • \(\sqrt{15} \approx 3.873\)
    • \(\frac{7}{3} \approx 2.333\)
    • \(0\)
    • \(-0.0123456\)
    • \(-\sqrt{45} \approx -6.708\) (smallest)

    Ordered from greatest to least: \(3\sqrt{27}, \sqrt{15}, \frac{7}{3}, 0, -0.0123456, -\sqrt{45}\)

  4. Fill in the blanks:

    • If I wanted to estimate \( \sqrt{59} \), the first step would be to find the two perfect squares that 59 lies between on the number line. The closest perfect square less than 59 is 49. The closest perfect square greater than 59 is 64. I could then think about the number 59 and how close it is to the smaller perfect square and the larger perfect square. I could then take the square root of the perfect squares to see how I would estimate \( \sqrt{59} \). The \( \sqrt{59} \) is closest to 8.

    Complete sentence: If I wanted to estimate \( \sqrt{59} \), the first step would be to find the two perfect squares that 59 lies between on the number line. The closest perfect square less than 59 is 49. The closest perfect square greater than 59 is 64. I could then think about the number 59 and how close it is to the smaller perfect square and the larger perfect square. I could then take the square root of the perfect squares to see how I would estimate \( \sqrt{59} \). The \( \sqrt{59} \) is closest to 8.