Introduction of Square Roots




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Introduction of square roots : The square root of a number a is that number which when multiplied by itself gives a as the product.
Thus, if b is the square root of a number a, then
b x b = a or b2 = a.
The square root symbol is √a
It follows from this that
b = √a ⇔ b2 = a.
i. e. b is the square root of a if and only if a is the square of b.

Example: 1) Square root of 16 is 4
(√16 = 4)
2) Square root of 3 is not a whole number.
(√3=1.73)
3)Square root of 9 is 3
(√9 = 3)
Example on finding the square roots :
(i) √ 4 = 2, because 22 = 4.
(ii) √9 = 3, because 32 = 9.
(iii) √324 = 18, because 182 = 324.
(iv) √1225 = 35, because 352 = 1225.
(v) √10,000 = 100, because 1002 = 10,000.
(vi) √a2 = a, because a2 = a x a.
Remark: Since 4 = 22 = (-2)2, therefore 2 and -2 can both be the square roots of 4.
However we agree that the square of a number will be taken to positive square root only . Thus, √4 = 2.

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Practice

1)√13x13 = -----
2) √c x c = -----
3) √19 x19 = -----
4) √(d x d x a x a) = -----
5) √10 x10 = -----
Squares and Square roots

Introduction of Squares and Square Roots
Perfect Squares or not
Properties of Square Numbers
Short cut method to find squares
Introduction of Square Roots
Properties of Square Roots
Square root by Prime factorization method
Square root by long division method
Square root of rational numbers
Square root of Decimals
Square root by estimation method

From squares and square roots to Exponents

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