Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Jan 16, 2024

Find the location of $\sqrt{31}$ on the number line, between 5 and 6.

STEP 1

Assumptions
1. We are to locate the square root of 31 on the number line.
2. We know that the square root of a number is a value that, when multiplied by itself, gives the original number.
3. We are considering whole numbers that are perfect squares close to 31 to help us estimate the position of the square root of 31.

STEP 2

Identify the perfect squares near 31 to establish a reference for the square root of 31.
$5^2 = 25$ $6^2 = 36$

STEP 3

Since 31 is between 25 and 36, we can conclude that the square root of 31 is between 5 and 6.
$5 < \sqrt{31} < 6$

STEP 4

To determine whether the square root of 31 is closer to 5 or 6, we can compare 31 to the mid-point between 25 and 36.
$Mid-point = \frac{25 + 36}{2}$

STEP 5

Calculate the mid-point.
$Mid-point = \frac{25 + 36}{2} = \frac{61}{2} = 30.5$

STEP 6

Since 31 is greater than 30.5, we can conclude that the square root of 31 is closer to 6 than to 5.
The square root of 31 should be located on the number line between 5 and 6 but closer to 6.

Was this helpful?

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Contact Influencer program Policy Terms