This GSEB Class 8 Maths Notes Chapter 6 Squares and Square Roots covers all the important topics and concepts as mentioned in the chapter.

## Squares and Square Roots Class 8 GSEB Notes

→ If a whole number is multiplied by itself, the product is called the square of a number.

For e.g. 1 × 1 = 1^{2}, 2 × 2 = 2^{2}, 3 × 3 = 3^{2},…

→ Perfect Square: A natural number is called a perfect square or a square number, if it is the product of the number with itself, e.g. 5 × 5 = 5^{2} = 25, 8 × 8 = 8^{2} = 64

→ Every number is not a perfect square, but there are infinite number of perfect squares.

→ If a number has 1 or 9 in its unit place, then its square ends in 1.

→ If a number has 2 or 8 in its unit place, then its square ends in 4.

→ If a number has 3 or 7 in its unit place, then its square ends in 9.

→ If a number has 4 or 6 in its unit place, then its square ends in 6.

→ If a number has 5 in its unit place, then its square ends in 5.

→ If a number has 0 in its unit place, then its square ends in two zeros (00).

→ If a number has 0 in its unit place and tens place, then its square ends in four zeros (0000).

→ Square of an even number is an even number while the square of an odd number is an odd number.

→ Square root is the inverse operation of square. Square root of a number is denoted by \(\sqrt{}\)

→ The square root of a number ‘x’ is that number, which when multiplied by itself gives ‘x’ as a product.

If, y2 = x :.y = \(\sqrt{x}\)

Here, ‘y’ is the square root of ‘x’ and ‘x’ is the square of ‘y’

→ Let us understand an important fact:

When we find square root of any number, a positive and a negative both integers are obtained.

e.g. (3)^{2} = 9 and (-3)^{2} = 9

But only positive square root of a number is denoted by ‘\(\sqrt{}\)‘

→ In this chapter, we shall be studying about positive square roots only (according to textbook).

\(\sqrt{4}\) =2(not – 2); \(\sqrt{9}\) = 3 (not – 3).

→ Square root of 81 are 9 and -9.

\(\sqrt{81}\) = 9 (not – 9)

i.e. when symbol ‘\(\sqrt{}\)’ is used, we take only positive root, but if wordings are used, we take both – positive as well as negative. 1 is the only number which is square as well as square root of itself.

→ Finding the square root through prime factorisation:

- Each prime factor in the prime factorisation of the square of a number, occurs twice the number of times it occurs in the prime factorisation of the number itself. Use this fact to find the square root of a number.
- If the given number is a perfect square, we will be able to make an exact number of pairs of prime factors. Product of one factor from each pair is the square root of a given number.
- Given number is not a perfect square if it has unpaired prime factors.

→ How to find square root of given numbers by division method :

- First, place a bar over every pair of digits starting from the digit at units place. Also, place a bar on the left most single digit if not forming a pair.
- Find the largest number whose square is less than or equal to the number under the extreme left bar. Take this number as divisor and the quotient with the number under the extreme left bar as the dividend.
- Divide and find the remainder. Bring down the number under the next bar the right of the remainder. Double the divisior and put it with a blank on its right.
- Continue this process till the remainder is zero and no bar left.