⁞ Square Roots And Cubes
Aptitude ➤ Square Roots And Cubes ➤ 1
Square Root: If x2 = y, we say that the square root of y is x and we write, √y = x.
Thus, √4 = 2, √9 = 3, √196 = 14.
Cube Root: The cube root of a given number x is the number whose cube is x. We denote the cube root of x by 3√x.
Thus, ∛8 = ∛2 x 2 x 2 = 2,
∛343 = ∛7 x 7 x 7 = 7 etc.
Note:
1.√xy = √x X √y
2. √(x/y) = √x / √y = (√x / √y) X (√y / √y) = √xy / y
Thus, √4 = 2, √9 = 3, √196 = 14.
Cube Root: The cube root of a given number x is the number whose cube is x. We denote the cube root of x by 3√x.
Thus, ∛8 = ∛
∛343 = ∛
Note:
1.√xy = √x X √y
2. √(x/y) = √x / √y = (√x / √y) X (√y / √y) = √xy / y
Question 1
Q1. Evaluate 6084.
Answer : 78
Factorization method : Express the given number as the product of prime factors.
Now, take the product of these prime factors choosing one out of every pair of the same primes. This product gives the square root of the given number.
Thus, resolving 6084 into prime factors, we get: 
6084 = 22 x 32 x 132
∴ 6084 = (2 x 3 x 13) = 78
⚔ DISCUSS
Question 2
Q2. Find the square root of 1471369.
Answer : 1213
In the given number, mark off the digits in pairs starting from the unit's digit. Each pair and the remaining one digit is called a period.
Now, 12 = 1. On subtracting, we get 0 as remainder.
Now, bring down the next period i.e., 47.
Now, trial divisor is 1 x 2 = 2 and trial dividend is 47.So, we take 22 as divisor and put 2 as quotient.
The remainder is 3.
Next, we bring down the next period which is 13.
Now, trial divisor is 12 x 2 = 24 and trial dividend is 313. So, we take 241 as dividend and 1 as quotient.
The remainder is 72.
Bring down the next period i.e., 69.
Now, the trial divisor is 121 x 2 = 242 and the trial dividend is 7269. So, we take 3 as quotient and 2423 as divisor.
The remainder is then zero.
Hence, 1471369 = 1213.
⚔ DISCUSS
Question 3
Q3. What is the square root of 0.0009 ?
Question 4
Q4. The cube root of 0.000216 is :
Question 5
Q5. The least perfect square, which is divisible by each of 21, 36 and 66 is :
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