Question

Directions: Simplify each radical

1. √20
3.√175
5.√72
7.-3√54
9.-5√98
expression.
2.√27
4.√50
6.-2√18
8.4√180
10.6√/112

Answer 1

To simplify each radical expression, find the largest perfect square that divides the number inside the square root evenly. Then, take the square root of that perfect square and multiply it by any number or variable outside the square root. Finally, simplify any remaining expressions.

Step-by-step explanation:

To simplify each radical expression, we need to find the largest perfect square that divides the number inside the square root symbol evenly. We can then take the square root of that perfect square and multiply it by any number or variable outside the square root symbol. Let's go through the steps for each radical expression:

1. √20: The largest perfect square that divides 20 evenly is 4. So we can simplify it as √(4 * 5), which is equal to √4 * √5. √4 is 2, so the simplified form is 2√5.
2. √27: The largest perfect square that divides 27 evenly is 9. So we can simplify it as √(9 * 3), which is equal to √9 * √3. √9 is 3, so the simplified form is 3√3.
3. √175: The largest perfect square that divides 175 evenly is 25. So we can simplify it as √(25 * 7), which is equal to √25 * √7. √25 is 5, so the simplified form is 5√7.
4. √50: The largest perfect square that divides 50 evenly is 25. So we can simplify it as √(25 * 2), which is equal to √25 * √2. √25 is 5, so the simplified form is 5√2.
5. -2√18: The largest perfect square that divides 18 evenly is 9. So we can simplify it as -2√(9 * 2), which is equal to -2√9 * √2. √9 is 3, so the simplified form is -2 * 3√2, which can be further simplified to -6√2.
6. √72: The largest perfect square that divides 72 evenly is 36. So we can simplify it as √(36 * 2), which is equal to √36 * √2. √36 is 6, so the simplified form is 6√2.
7. 4√180: The largest perfect square that divides 180 evenly is 36. So we can simplify it as 4√(36 * 5), which is equal to 4√36 * √5. √36 is 6, so the simplified form is 4 * 6√5, which can be further simplified to 24√5.
8. -5√98: The largest perfect square that divides 98 evenly is 49. So we can simplify it as -5√(49 * 2), which is equal to -5√49 * √2. √49 is 7, so the simplified form is -5 * 7√2, which can be further simplified to -35√2.
9. 6√112: The largest perfect square that divides 112 evenly is 16. So we can simplify it as 6√(16 * 7), which is equal to 6√16 * √7. √16 is 4, so the simplified form is 6 * 4√7, which can be further simplified to 24√7.