In mathematics, square that a number is the an outcome of multiplying the number through itself. The word square is usually equivalent to raising a number to the power of 2 and also denoted by the superscript 2.

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For example, the square that 4 is created as 42 which provides 16 as the answer. In this case, 16 is the square that number 4.

Below is a list of squares that the an initial twelve numbers:

1 x 1 = 1 7 x 7 = 492 x 2 = 4 8 x 8 = 643 x 3 = 9 9 x 9 = 814 x 4 = 16 10 x 10 = 1005 x 5 = 25 11 x 11 = 1216 x 6 = 36 12 x 12 = 144

### Squaring negative Numbers

The square that a an unfavorable number is a hopeful number. For instance, -3 x -3 would end up being 9, however – 3 x 3 = -9, this is since -3 is a various number to 3.

## What is Square root of a Number?

The square source is one inverse procedure of squaring a number. In other words, the square source is an procedure that undoes one exponent the 2. A square source of a number x is such that a number y is the square of x, simplify created as y2 = x.

For example, 5 and also – 5 are both square root of 25 because:

5 x 5 = 25 and also -5 x -5 =25.

The square source of a number x is denoted v a radical authorize √x or x 1/2. Because that instance, the square root of 16 is stood for as √16 = 4. A number who square source is calculated is described as radicand. In this expression, √16 = 4, number 16 is the radicand.

### Properties

A perfect square number has actually a perfect square root.An also perfect number has actually the square root the is even.The odd perfect number has actually the square root the is odd.The square root of a an adverse number is undefined.Only numbers finishing with one even variety of zeros have square roots.

### Finding the Square source of Numbers

Repeated Subtraction:This technique involves successful and repeated subtraction of odd number such together 1, 3, 5, and also 7 native the number until zero is reached. The square of the number is same to the number or frequency of individually performed ~ above the number. Suppose we should calculate the square of a perfect number favor 16, the variety of subtractions performed is 4, so the square root of 16 is 4.Prime Factorization:In this method, a perfect square number is factorized by succeeding divisions. The prime determinants are grouped into pairs, and also the product of every number is calculated. The product is therefore, the square source of the number. To uncover the square the a perfect number such as: 144 is carry out as:144 = 2 × 2 × 2 × 2 × 3 × 3.Pair the prime factors.Selecting one number from every pair.2 × 2 × 3 = 12.Thus, the √144 = 12.Division Method:Division an approach is a suitable technique of calculating the square the a huge number.The adhering to are the procedures involved:A bar is placed over every pair that digits beginning from the right-hand side.Divide left end number by a number who square is less or identical to the number under the left end.Take this number together the divisor and also quotient. Similarly, take it the outward number as the dividend.Divide to get the result.Pull under the following number v a bar come the right-hand next of the remainder.Multiply the divisor by 2.To the best of this brand-new divisor, find a perfect dividend. This process is repetitive until we obtain zero as the remainder. The square of the number because of this is same to the quotient.

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Practice Questions

1. Write down the worth of

(a) √81

(b) √1

(c) √121

(d) √0

2. Identify square numbers from the complying with list that numbers:2 6 11 14 16 18 24 25.

3. Create down the value of (a) 3² (b)6 squared c) 8² (d) 9 squared (e) 12²

4. Ns am is reasoning of two numbers. Both numbers space square numbers higher than 1. If the amount of this numbers is 100. What room the 2 numbers?