Question

Find a rational number one with a decimal place that is between square root 17 and square root 18

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find a rational number between √17 and √18, we first want to find the exact values of these square roots. By using a calculator, we get:

√17 ≈ 4.123105625617661
√18 ≈ 4.242640687119285

To find a rational number in between these two values, we can rationalize the denominators of the square roots. We can multiply both the numerator and denominator of each square root by the conjugate of the denominator to get rid of the square root sign. It will look like this:

√17 * (√17 / √17) = √(17*17) / √17 = 17 / √17
√18 * (√18 / √18) = √(18*18) / √18 = 18 / √18

Now, we need to simplify these expressions:

17 / √17 ≈ 17 / 4.123105625617661 ≈ 4.125
18 / √18 ≈ 18 / 4.242640687119285 ≈ 4.243

Thus, we have found a rational number (with one decimal place) that is between √17 and √18, which is approximately 4.2.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To find a rational number between the square roots of 17 and 18, we can start by estimating the square roots of these numbers.

The exact value of √17 is approximately 4.1231, and the exact value of √18 is approximately 4.2426.

Let's consider a decimal number between these two values, such as 4.2. We'll square this decimal to determine if it falls between 17 and 18:

(4.2)^2 = 17.64

Since 17 < 17.64 < 18, we know that 4.2 is not above the square root of 18.

Regarding finding a rational number, we can write the decimal number 4.2 as a fraction:

4.2 = 42/10 = 21/5

So, the rational number between √17 and √18 would be 21/5 or 4.2.