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Home >> Cube Root >> Cube Root by Shortcut Method >>

Cube Root by Shortcut Method

 Cube Root by Prime Factorization Method Cube Root by Shortcut Method

 Before you study this concept, you are adviced to read: What are Cube Numbers ? What is a Cube Root ? What are the Properties of Cube Numbers ? Steps of this shortcut method are: Step 1: Make group of three digits starting from the digit at one's place of the given cube number (if the given number have five digit, you can make first group comprising three digits and second group comprising two digits) Step 2: Take First Group -- Digit at One's place of first group will help you to find digit at one's place of the cube root.(For this you must study all the properties of cube numbers) Step 3: Take Second Group - Find the number whose cube number is nearest & less than the number of second group and this number will be the digit at ten's place of the cube root Step 4: Result of step 2 and step 3 gives you cube root of the given number. (Note: This shortcut method applies to only perfect cubes and not on non-perfect cubes) Example 1: Find cube root of 13824 using shortcut method Solution: Steps of find cube root are as follows: Step 1: Make group of three digits starting from the digit at one's place, of the given cube number ( if the given number have five digit, you can make first group comprising three digits and second group comprising two digits.) Here the given cube number has five digits, so we get following two groups: First Group = 824 Second Group = 13 Step 2: Take First Group -- Digit at One's place of first group will help you to find digit at one's place of the cube root. First Group = 824 One's place digit of this first group = 4 As per the Property 4 of Cube Number :- Cube of Natural Number ending with 4, also ends with 4. So, this means that cube root of given number 13824 will certainly have 4 at its one's place. Step 3: Take Second Group - Find the number whose cube number is nearest & less than the number of second group and this number will be the digit at ten's place of the cube root Second Group = 13 Cube of 2 = 8 and 8 is the nearest & less than 13 (If we take 3 its cube is 27, which is also nearest but more than 13) So, this means that cube root of given number 13824 will certainly have 2 at its ten's place. Step 4: Result of step 2 and step 3 gives you cube root of the given number. From Step 2 we get: Digit at one's place = 4 From Step 3 we get: Digit at ten's place = 2 Hence, cube root of 13824 = 24 Example 2: Find cube root of 175616 using shortcut method Solution: Steps of find cube root are as follows: Step 1: Make group of three digits starting from the digit at one's place of the given cube number Two groups: First Group = 616 Second Group = 175 Step 2: Take First Group -- Digit at One's place of first group will help you to find digit at one's place of the cube root. First Group = 616 One's place digit of this first group = 6 As per the Property 6 of Cube Number :- Cube of Natural Number ending with 6, also ends with 6. So, this means that cube root of given number 175616 will certainly have 6 at its one's place. Step 3: Take Second Group - Find the number whose cube number is nearest & less than the number of second group and this number will be the digit at ten's place of the cube root Second Group = 175 Cube of 5 = 125 and 125 is the nearest & less than 175 (If we take 6 its cube is 216, which is also nearest but more than 175) So, this means that cube root of given number 175616 will certainly have 5 at its ten's place. Step 4: Result of step 2 and step 3 gives you cube root of the given number. From Step 2 we get: Digit at one's place = 6 From Step 3 we get: Digit at ten's place = 5 Hence, cube root of 175616 = 56 Example 3: Find cube root of 110592 without using calculator Solution: Steps of find cube root are as follows: Step 1: Make group of three digits starting from the digit at one's place of the given cube number Two groups: First Group = 592 Second Group = 110 Step 2: Take First Group -- Digit at One's place of first group will help you to find digit at one's place of the cube root. First Group = 592 One's place digit of this first group = 592 As per the Property 8 of Cube Number :- Cube of Natural Number ending with 8, ends with 2. So, this means that cube root of given number 110592 will certainly have 8 at its one's place. Step 3: Take Second Group - Find the number whose cube number is nearest & less than the number of second group and this number will be the digit at ten's place of the cube root Second Group = 110 Cube of 4 = 64 and 64 is the nearest & less than 110 (If we take 5 its cube is 125, which is also nearest but more than 110) So, this means that cube root of given number 175616 will certainly have 4 at its ten's place. Step 4: Result of step 2 and step 3 gives you cube root of the given number. From Step 2 we get: Digit at one's place = 8 From Step 3 we get: Digit at ten's place = 4 Hence, cube root of 110592 = 48 Example 4: Find cube root of 300763 without using calculator Solution: Steps of find cube root are as follows: Step 1: Make group of three digits starting from the digit at one's place of the given cube number Two groups: First Group = 300 Second Group = 763 Step 2: Take First Group -- Digit at One's place of first group will help you to find digit at one's place of the cube root. First Group = 763 One's place digit of this first group = 763 As per the Property 7 of Cube Number :- Cube of Natural Number ending with 7, ends with 3. So, this means that cube root of given number 110592 will certainly have 7 at its one's place. Step 3: Take Second Group - Find the number whose cube number is nearest & less than the number of second group and this number will be the digit at ten's place of the cube root Second Group = 300 Cube of 6 = 216 and 216 is the nearest & less than 300 (If we take 7 its cube is 343, which is also nearest but more than 300) So, this means that cube root of given number 175616 will certainly have 6 at its ten's place. Step 4: Result of step 2 and step 3 gives you cube root of the given number. From Step 2 we get: Digit at one's place = 7 From Step 3 we get: Digit at ten's place = 6 Hence, cube root of 300763 = 67

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