Final answer:
10 sqrt(5) is between the integers 20 and 30, since the square root of 5 falls between 2 and 3 and is multiplied by 10.
Step-by-step explanation:
The question asks to determine which two integers the expression 10 sqrt(5) falls between. To find this, we need to estimate the square root of 5. We know that sqrt(4) is 2 and sqrt(9) is 3. Since 5 is between 4 and 9, sqrt(5) must be between 2 and 3. Thus, 10 times the square root of 5 must be between 10*2 and 10*3, which are 20 and 30, respectively.
Therefore,
10 sqrt(5)
is between the integers 20 and 30. Our reasoning is based on the known square roots of perfect squares that are adjacent to 5, and scaling those square roots by the factor of 10 which is outside the radical sign.