If any number is expressed as x × x, then x is the product of two same numbers. We know that 5^2 = 5× 5 =25.Here 25 is called the square of 5 and 5 is called the square root of 25. And (2/3)^2 = (2/3)× (2/3) = 2 ×2/3 ×3 = 4/9. 4/9 is called as square of 2/3 and is also called as square root of 4 / 9.
Examples of Solving Root of a Number
1. Simplify 7^2 = 7 ×7 = 49
Here 49 is called the square of 7 and 7 is called the square root of 49
2. (0.4)^2 = (0.4)× (0.4) = 0.16
Here 0.16 is called the square of 0.4 and 0.4 is called the square root of 0.16
3. Simplify 9^2 = 9 ×9 = 81
Here 81 is called the square of 9 and 9 is called the square root of 81
4. Simplify 121^2 = 121 ×121 = 14641
Here 14641 is called the square of 7 and 7 is called the square root of 14641
5. Simplify 81^2 = 81 ×81= 49
Here 6561 is called the square of 81 and 81 is called the square root of 6561
Multi Step Square Root Examples:
(1). Find the square root of 144
Solution:
Split the number into the product of prime factors.
144 = 3 × 3 × 2 × 2 × 2 × 2
√144 = √3^2 × 2^2 × 2^2
=3 × 2 × 2
Therefore √144 = 12
(2). Find the square root of 5^3 × 5^5
Solution:
5^3 × 5^5 = (5 × 5 × 5) × (5 × 5 × 5 × 5 × 5)
=5^2 × 5^2 × 5^2 × 5^2
Therefore √5^3 × 5^5 = √5^2 × 5^2 × 5^2 × 5^2
= 5 × 5 × 5 × 5 × 5
= 625
Therefore √5^3 × 5^5 = 625
Discuss of Solving Root of Number
(1) Find the square root of 36
(2) Find the square root of 6^2×7^2
(3) Find the square root of 8100
Answers:
1. 6 2. 42 3. 90
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