1. Find the square root of 196: √196
2. Find the square root of 625: √625
3. What is the symbol that denotes a root (called the radical)?
4. Find the cube root of -125: ^3√-125.
5. When you take the cube root of a negative number, is the sign of the cube root positive (+) or negative (–)?
1. The square root of 196 is 14.
2. The square root of 625 is 25.
3. The symbol that denotes a root (called the radical) is √.
4. The cube root of -125 is -5.
5. When you take the cube root of a negative number, the sign of the cube root is negative (–).
1. The square root of 81 is 9.
2. The square root of 100 is 10.
3. The cube root of 512 is 8.
4. The cube root of -343 is -7.
5. The cube root of 81 is 4.
The correct answer for the last one is: 2 square root of 81
1. To find the square root of 196 (√196), we need to find a number that, when multiplied by itself, equals 196.
The square root of 196 is 14, because 14 * 14 = 196.
2. To find the square root of 625 (√625), we need to find a number that, when multiplied by itself, equals 625.
The square root of 625 is 25, because 25 * 25 = 625.
3. The symbol that denotes a root is called a radical (√). It is used to represent the operation of finding the root of a number.
4. To find the cube root of -125 (^3√-125), we need to find a number that, when multiplied by itself three times, equals -125.
The cube root of -125 is -5, because -5 * -5 * -5 = -125.
5. When you take the cube root of a negative number, the sign of the cube root is negative (–). This means that the result will be negative.
1. To find the square root of 196 (√196), you can use a calculator or use the method of prime factorization. For prime factorization, start by finding the prime factors of 196, which are 2 and 7. Write the number as the product of these primes: 196 = 2^2 * 7^2. Since the square root represents finding a number that, when multiplied by itself, equals 196, you can take the square root of both the base (2) and the exponent (2) of each prime factor: √(2^2 * 7^2) = 2 * 7 = 14. Therefore, the square root of 196 is 14.
2. To find the square root of 625 (√625), you can again use a calculator or use the method of prime factorization. The prime factors of 625 are 5^2. Taking the square root of both the base (5) and the exponent (2) of this prime factor, √(5^2) = 5. Therefore, the square root of 625 is 5.
3. The symbol used to denote a root, particularly the square root, is called a radical. It looks like the symbol √.
4. To find the cube root of -125 (^3√-125), you can use a calculator or use the fact that any number multiplied by itself three times equals the original number. Since (-5)^3 = -125, the cube root of -125 is -5. So, the cube root of -125 is -5.
5. When you take the cube root of a negative number, the sign of the cube root depends on the number being cube-rooted. If the number being cube-rooted is negative, the sign of the cube root will also be negative. In the example above, the number being cube-rooted is -125, so the cube root is -5.
1. Find the square root of 81: √81
2. Find the square root of 100: √100
3. Find the cube root of 512: ^3√512
4. Find the cube root of -343: ^3√-343
5. Find the cube root of 81: ^3√81
5. Find the cube root of 81: ^3√81
^3√81
-9
27
9