Question

5. Cube root of 64 is..........​

Answer 1

4 .

hope it help u........

Answer 2

Cube root of 64, 3√64 = 4

Let us say, ‘m’ is equal to 3√64, then m × m × m = m3 = 64 (as per the definition of the cube). Since 64 is a two-digit number, we can use here prime factorisation method to find its cube root. Let us learn how to calculate it, without using a calculator.

Step 1: By prime factorisation of 64, we get;

Step 1: By prime factorisation of 64, we get;64 = 2 × 2 × 2 × 2 × 2 × 2

Step 2: Pair the factors of 64 in a group of three, such that they form cubes.

Step 2: Pair the factors of 64 in a group of three, such that they form cubes.64 = (2 × 2 × 2) × (2 × 2 × 2)

Step 2: Pair the factors of 64 in a group of three, such that they form cubes.64 = (2 × 2 × 2) × (2 × 2 × 2)64 = 23 × 23

Step 2: Pair the factors of 64 in a group of three, such that they form cubes.64 = (2 × 2 × 2) × (2 × 2 × 2)64 = 23 × 23Using the law of exponent, we get;

Step 2: Pair the factors of 64 in a group of three, such that they form cubes.64 = (2 × 2 × 2) × (2 × 2 × 2)64 = 23 × 23Using the law of exponent, we get;64 = 23+3 = 26 [am.an = (a)m+n]

Step 2: Pair the factors of 64 in a group of three, such that they form cubes.64 = (2 × 2 × 2) × (2 × 2 × 2)64 = 23 × 23Using the law of exponent, we get;64 = 23+3 = 26 [am.an = (a)m+n]Or

Step 2: Pair the factors of 64 in a group of three, such that they form cubes.64 = (2 × 2 × 2) × (2 × 2 × 2)64 = 23 × 23Using the law of exponent, we get;64 = 23+3 = 26 [am.an = (a)m+n]Or64 = (22)3 [(am)n = amn]

Step 2: Pair the factors of 64 in a group of three, such that they form cubes.64 = (2 × 2 × 2) × (2 × 2 × 2)64 = 23 × 23Using the law of exponent, we get;64 = 23+3 = 26 [am.an = (a)m+n]Or64 = (22)3 [(am)n = amn]64 = 43

Step 3: Now, we will take the cube root on both sides of the above expression.

Step 3: Now, we will take the cube root on both sides of the above expression.3√64 = 3√(43)

Step 3: Now, we will take the cube root on both sides of the above expression.3√64 = 3√(43)So, here the cube root is eliminated by the cube of 4.

Step 3: Now, we will take the cube root on both sides of the above expression.3√64 = 3√(43)So, here the cube root is eliminated by the cube of 4.Hence, we get the value of cubic root of 64, i.e.,

Step 3: Now, we will take the cube root on both sides of the above expression.3√64 = 3√(43)So, here the cube root is eliminated by the cube of 4.Hence, we get the value of cubic root of 64, i.e.,3√64 = 4

Step 3: Now, we will take the cube root on both sides of the above expression.3√64 = 3√(43)So, here the cube root is eliminated by the cube of 4.Hence, we get the value of cubic root of 64, i.e.,3√64 = 4Since 64 is a perfect cube, therefore it is easy to find its cube root, but for imperfect cubes we have to estimate the values. But it sometimes becomes difficult to evaluate.

Step 3: Now, we will take the cube root on both sides of the above expression.3√64 = 3√(43)So, here the cube root is eliminated by the cube of 4.Hence, we get the value of cubic root of 64, i.e.,3√64 = 4Since 64 is a perfect cube, therefore it is easy to find its cube root, but for imperfect cubes we have to estimate the values. But it sometimes becomes difficult to evaluate.Below is the table of cubes of 1 to 10 numbers to find the cube root easily