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Answer 1

Answer:

Finding the square root of a number by estimating and multiplying can be a long procedure. Given below is a simpler method to find the square root of a number:

Example: Find the square root of 2116

To find the square root of 2116:

Step 1: See the digit at one’s place. In this case, it is 6. Now, check between 1-9, the square of what all numbers have “6” at one’s place. The answer is 42 = 16 and 62 = 36

Step 2: Now check, the square of which number between 1 to 9 is closest to the first two digits of the given number. In this case, the sum of which number between 1 to 9 is closest to 21. The answer is 42 = 16 and 52 = 25

So, one number among 44, 46, 54 and 56 is the square root of 2116

Step 3: The two numbers you got in step 2, multiply each of them with the next number in the number series. That is, 4×5 = 20 and 5×6 = 30. Since 20 is a closer number to 21. The answer has to be either 46 or 44. Multiply and check your answer.

Check yourself with the below-mentioned example:

Example: What is the square root of 1024?

Solution:

Step 1: 22 = 4 and 82 = 64

Step 2: 32 = 9

Step 3: 3×4 = 12. Since 12 is greater than 10. So the square root will be 32.

2. Cube Root

Follow the steps given below to quickly find out the cube root of a number.

Example: What is the cube root of 9261

Step 1: Find the numbers between 1 to 9 whose cube is equal to the digit present at the one’s place, here it is 1. So, we get 1×1×1 = 1

Step 2: See the first digit of the number, in this case, 9. 9 lies between the cube of 2 (2×2×2=8) and (3×3×3 = 27). Since 8 is closest to 9. Cube root of 9261 is 21.

Note: To find the cube root of 5 digit number, use the first two digits instead of the first digit in step 2

Try one example by yourself to understand the trick even better:

Example: What is the cube root of 32768

Step 1: 23 = 8

Step 2: 33 = 27 and 43 = 64

Since 27 is closer to 32, the cube root of 32768 will be 32.

Candidates who are looking for shortcut tricks to calculate the square & cube of a number can visit the linked article.

3. Quadratic Equations

Given below are two examples of quadratic equations solved with easy tricks to find the answer quickly:

Example: x² – 18x + 45 = 0

Step 1: Multiply the coefficient of x² and the constant in the equation. In this case, 1×45 = 45

Step 2: Multiply “-1” with the coefficient of x. In this case, -1× (-18) = 18

Step 3: Hence, the value of x will be 15 and 3 (3+15=18 & 3×15=45). Remember, for signs, if the answer obtained in both step 1 & 2 is positive, then both values of x will be positive. If even one is negative, then values of x will be negative.

Here, the value obtained in step 1 & 2 is positive hence the value of x will be positive. So, the answer is x = 15, 3

Example: x²-5x-6 = 0

Step 1: Multiply the coefficient of x² and the constant in the equation. In this case, 1×(-6) = (-6)

Step 2: Multiply “-1” with the coefficient of x. In this case, (-1)× (-5) = 5

Step 3: Hence, the value of x will be 6 and 1 (6-1=5 & 6×1=6). Remember, for signs, if the answer obtained in both step 1 & 2 is positive, then both values of x will be positive. If even one is negative, then one of the values of x will be negative.

Step 4: Here the answer in step 1 is negative. Thus, one value of x will be negative. If the answer in step 1 is negative, the smaller value of x will be negative. If the answer in step 2 is negative, the larger value will be negative.

So, x= 6, -1

Learn more about such equations and get the top Tips to Solve Quadratic Equations at the linked article.