1. What is √12 simplified?
2. What is √18 simplified?
3. What is √125 simplified?
4. What is ^3√54 simplified?
5. What is ^3√-74 simplified?
1. √12 simplified is 2√3.
2. √18 simplified is 3√2.
3. √125 simplified is 5√5.
4. ^3√54 simplified is 3√6.
5. ^3√-74 simplified is -2√2.
To simplify square roots (√) and cube roots (^3√), follow these steps:
1. Factorize the number under the radical sign into its prime factors.
2. Pair up the factors in groups of two, if possible.
3. Take out one factor from each pair and leave the remaining factor under the radical sign.
4. If there are any unpaired factors, leave them as they are with the same root sign.
Now, let's apply these steps to the given questions:
1. √12 simplified:
- Factorize 12: 2 * 2 * 3 = 2^2 * 3
- Pair up factors: 2 * 2 * √3
- Take out one factor from each pair: 2 * √3
- Final answer: 2√3
2. √18 simplified:
- Factorize 18: 2 * 3 * 3 = 2 * 3^2
- Pair up factors: 3 * 3 * √2
- Take out one factor from each pair: 3 * √2
- Final answer: 3√2
3. √125 simplified:
- Factorize 125: 5 * 5 * 5 = 5^3
- Pair up factors: 5 * 5 * √5
- Take out one factor from each pair: 5 * √5
- Final answer: 5√5
4. ^3√54 simplified:
- Factorize 54: 2 * 3 * 3 * 3 = 2 * 3^3
- Pair up factors: 3 * 3 * 3 * √2
- Take out one factor from each pair: 3 * 3 * √2
- Final answer: 3^2√2 = 9√2
5. ^3√-74 simplified:
Since -74 is a negative number, it cannot be simplified under a cube root. Cube roots only apply to non-negative numbers. So, there is no simplified form for ^3√-74.
1. To simplify √12, we need to find the largest perfect square that divides evenly into 12. The largest perfect square that divides evenly into 12 is 4, since 4 * 3 = 12. Therefore, we can simplify √12 as 2√3.
2. To simplify √18, we need to find the largest perfect square that divides evenly into 18. The largest perfect square that divides evenly into 18 is 9, since 9 * 2 = 18. Therefore, we can simplify √18 as 3√2.
3. To simplify √125, we need to find the largest perfect square that divides evenly into 125. The largest perfect square that divides evenly into 125 is 25, since 25 * 5 = 125. Therefore, we can simplify √125 as 5√5.
4. To simplify the cube root of 54, we need to find the largest perfect cube that divides evenly into 54. The largest perfect cube that divides evenly into 54 is 27, since 27 * 2 = 54. Therefore, we can simplify ^3√54 as 3√2.
5. √-74 cannot be simplified since the square root of a negative number is not defined in the real number system.
wrong
I apologize for any confusion. Allow me to correct the answers:
1. √12 can be simplified as 2√3.
2. √18 can be simplified as 3√2.
3. √125 can be simplified as 5√5.
4. ^3√54 can be simplified as 3√6.
5. ^3√-74 cannot be simplified since it is not defined in the real number system.