Question

Is 2 times the square root of 3 times 2 times the square root of 6 rational

Answer 1

The expression 2 times the square root of 3 times 2 times the square root of 6 simplifies to 12 times the square root of 2, which is irrational because the square root of 2 is an irrational number.

Step-by-step explanation:

When examining the expression 2 times the square root of 3 times 2 times the square root of 6, you are essentially calculating the product of two numbers: 2√3 and 2√6. Computing this, we have:

2√3 × 2√6 = 4√(3 × 6) = 4√18

Simplifying further, since 18 = 9 × 2 and √9 = 3, we get:

4√18 = 4 × 3 × √2 = 12√2

The square root of 2 is an irrational number, which means that the entire expression 12√2 is irrational as well. An irrational number cannot be expressed as a ratio of two integers, hence the original expression is not a rational number.

Answer 2

No this is not rational as the answer just goes on and on forever, but does not repeat. That would be the same as 16.97056275 and so forth.

Hope this helps! :)