Final answer:
The square root of 121 is 11, which is a rational number. The square root of 48 simplifies to 4√3, which is an irrational number.
Step-by-step explanation:
Simplifying Square Root ExpressionsTo simplify the square root of 121, we look for a perfect square that is a factor of 121. Since 121 is itself a perfect square (11²), the square root of 121 is 11, which is a rational number.Next, for the square root of 48, we break it down into its prime factors which are 2² × 2² × 3. We can take out the pairs of 2 as a single 2, so we have 2 × 2 × √3, which simplifies to 4√3.
The number 4 is rational, but √3 is irrational, so the simplified form, 4√3, is irrational as wellTherefore, √121 is rational and √48 is irrational when simplified.The square root of 121 is equal to 11. This is because 11 multiplied by itself equals 121. So, the square root of 121 is rational.The square root of 48 can be simplified as 4√3. This is because 16 is a perfect square factor of 48, so we can write it as 16√3, which is equal to 4√3. Therefore, the square root of 48 is irrational.