To find the square root of a number, you're looking for a value that, when multiplied by itself, equals the original number (e.g., √49 is 7 because 7 x 7 = 49). You can find this using estimation, prime factorization (for perfect squares), the long division method, or modern tools like calculators, with the goal being to find that "self-multiplying" number.
Common Square Root Tricks
Pair the digits: Group the given number into pairs from the right. For example, 4761 becomes (47) (61). Check last digit pattern: The units digit of the square root comes from observing the last digit of your number (for example, numbers ending in 9 have square roots ending in 3 or 7).
The square root of 64 is 8.
We know that √49 is 7.
The square root of 100 is 10.
Cube root of 64, 3√64 = 4
Since 64 is a two-digit number, we can use here prime factorisation method to find its cube root.
The square root of 8 is 2.82842.
The value of the cube root of 3 is equal to 1.44224957031. Cube root of 3 in radical form is represented as 3√3 and in exponential form as 31/3. Since 3 is not a perfect cube, therefore it is a little difficult to find its cube root.
We can use any of the above methods for finding the square root, such as prime factorization, and so on. 91/2 = √9 = √(3×3) = 3. So, the formula for writing the square root of a number is √x= x1/2.
Fractional exponents
In other words, taking a number to the power of 12 is the same thing as taking a square root: x1/2=√x. Since (xn)1/n=x1=x, we can generalize the result so that taking a number to the power of 1/n is the same thing as taking the nth root: x1/n=n√x.
Cube root of number is a value which when multiplied by itself thrice or three times produces the original value. For example, the cube root of 27, denoted as 3√27, is 3, because when we multiply 3 by itself three times we get 3 x 3 x 3 = 27 = 33.
We want to find numbers that are both perfect squares and perfect cubes. For example, 64 is a perfect square since 82=64 and also a perfect cube since 43=64.
Obtain the prime factorization of the given natural number. Make pairs of identical factors. Take one factor from each pair and find their product. The product so obtained is the square root of the given number.
Square root of 144, √144 = 12
As per the given expression above, we can define the square root of natural number 144, is a value which on multiplying by itself gives 144.
The square root of 70 is 8.3666.
Find the unit digits we get after squaring the numbers from 1 to 10 in the below table. Hence, from the above table we can figure out if any perfect square ends with the above digits at the unit place, then its square root will have the same respective number at the unit place. For example, the square root of 81 is 9.
What is the square root of 48 in simplified form? The square root of 48 in simplified form is 4√3.
Square Root of 49 Solved Examples
-(√49) has real roots but (-√49) has only imaginary roots.