Introduction of Square Roots

Enter your number: The square root is : The square of a number is :

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.

_______________________________________________________________
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

Home Page