## Root Table

A Square Root Table is a table of square roots that shows all the natural numbers from 1 to 100, each approximately to 3 places of decimal. Using the square root table, we can find the square roots of numbers, less than 100. Square root tables are used to determine the approximate values. The method of long division is difficult and lengthy to find the square root of a number. To make it easier, tables containing a list of approximate values of the square roots for certain different numbers have been prepared for convenience. You can write the square root in a table. Every positive number has two square roots: √x which is positive, and -√x which is negative. For example, the value of root 3 is 1.732.

### Properties of a Square Root

A perfect square number will have a perfect square root.

An even perfect number has an even square root.

An odd perfect number has a square root that is odd.

The value of a negative number’s square root is undefined.

Only numbers ending with even numbers of zeros have square roots.

### Cube Root

The cube root of a given number x is a number y such that y3 = x. As much as it is important to know the square root and cube root of a number, you should also know the cube root 1 to 50 of the first 50 natural numbers.

Square root table 1 50 is also as important involving 1 to 50 square root as the table for cube roots upto 50. The root table or chart helps us learn and understand some of the basic operations of mathematics. For beginners, who are getting started with square roots and cube roots, square root table 1 30 which contains square root till 30 natural numbers can help to get acquainted with the topic.

### Finding the Square Root of a Number

Repeated Subtraction: The method of repeated subtraction denotes the successful and repeated subtraction of odd numbers(like 1, 3, 5, and 7) from the given number until it reaches zero. The square of a given number is equal to the frequency of subtraction performed on the number. Let us say, we need to calculate the square of a perfect number. For a perfect number like 16, the number of removals that is performed is 4, there, the square root of 16 is 4.

Prime Factorization: In this method, a perfect square number is factorized by successive division. The prime factors are usually grouped into pairs after which the product of each number is calculated. Therefore, the product is the square root of the number.

Division Method: The division method is a suitable technique for calculating the square of a large number. The following are the steps are involved:

Over every pair of digits, starting from the right-hand side, a bar is placed.

Divide the number present at the left end by a number whose square is less than or equivalent to the numbers present under the left end.

Take this number as the divisor and quotient. Similarly, take the leftmost number as the dividend.

Divide to get the result.

To the right-hand side of the remainder, you need to pull down the next number along with a bar.

Multiply the divisor by 2.

To the right of this new divisor, find an eligible dividend. This process gets repeated until we find zero as the remainder. The square of the number becomes equal to the quotient.

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The square root chart from the numbers 1 to 50. It is also known as the square root table for the first 50 natural numbers.

## Square Root up to 50

### Solved Example on Square Root 1 to 50

Q. Find the square root of 48.

Answer: √48 = √16 * √3

= 4 * √3

= 4√3

= 6.928

Q. Find the square root of 18.

Answer: 18 = √9 * √2

= 3 * √2

= 3√2

= 4.243

Q1. Write the Difference Between Square and Square Root of a Number.

Answer: **Square of a Number:** In mathematics, the square of a number is the result of multiplying the number by itself. The word square is usually equivalent to raising a number to the power of 2 and denoted by the superscript 2. For example, the square of the number 4 is written as 42, which gives 16 as the answer. The square of the number 4 is 16, in this case.

**Square Root of a Number:** A square root of a given number x is a number y such that, y^{2} = x; in simpler words, a number y whose square (the result of multiplying the said number by itself, or y * y) is x. To show you as an example, 4 and −4 are square roots of 16, because 42 = (−4)^{2} = 16. Every given non-negative real number x contains a unique non-negative square root, that is denoted by √x, where the symbol √ is known as the radical sign or radix. To show you as an example, the principal square root of number 9 is 3, which is denoted by √9 = 3 because 32 = 3 * 3 = 9 and 3 is non-negative. The considered square root of a number (or term) is known as the radicand. The radicand is known as the number or expression placed underneath the radical sign, which is 9 in this case.

Q2. Briefly Describe the Square Root of a Number.

Answer: Square root is an inverse operation of the squaring of a number. In other terms, the square root is an operation that undoes an exponent of 2. A square root of a number x is such that, a number y is the square of x, simply written as y^{2} = x. For example, 4 and -4 are both square roots of 16 as 4*4 = 16 and -4*-4 = 16. The square root of a number x is denoted with a radical sign √x or x^{1/2}. For instance, the square root of 16 is represented as √25 = 5. A number whose square root is calculated is called a radicand. In this example, √25 = 5 number 25 is the radicand.