Using rational approximations, what statement is true?

Question

√49>7

√49<7
√48>√36

√48<√36

Answer 1

To evaluate the statements, let's analyze each one carefully:

1. √49 > 7:

   • We know that √49 = 7. Therefore, this statement is false.

2. √49 < 7:

   • Since √49 = 7, this statement is also false.

3. √48 > √36:

   • We know that √36 = 6. To find √48, we can recognize that √48 is approximately √(4×12) = 2√12. The value of √12 is around 3.464, so 2√12 is approximately 6.928. Since 6.928 > 6, this statement is true.

4. √48 < √36:

   • Given that √48 > 6, this statement is false.

From the analysis above, the true statement is:

√48 > √36.

Answer 2

are you sure

Answer 3

Let's carefully reevaluate the comparisons to ensure accuracy.

1. √49 > 7:

   • √49 = 7, so this is false.

2. √49 < 7:

   • Again, since √49 = 7, this is false.

3. √48 > √36:

   • We know that √36 = 6. Now for √48, we can simplify it to: \[ \sqrt{48} = \sqrt{16 \times 3} = 4\sqrt{3} \]
   • We know that √3 is approximately 1.732. Therefore, \[ 4\sqrt{3} \approx 4 \times 1.732 \approx 6.928 \]
   • Since 6.928 > 6, this statement is true.

4. √48 < √36:

   • This is the opposite of the prior statement, and since we've established that √48 > √36, this is false.

So, to confirm, the statement that is true is indeed:

√48 > √36.

Thank you for your patience, and the conclusion remains accurate.