Square Roots Of Decimals
Chapter Name : Squares And Square Roots |
Sub Topic Code : 104_08_06_06_01 |
Topic Name : Square Roots Of Decimals |
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Sub Topic Name : Square Roots Of Decimals |
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Introduction
What is a square root?
Pre-Requisites:
Basic knowledge about arithmetic operations, square numbers and square roots
Activity:
A square number is represented with bars and the one’s digit is considered. A square root of a square less than that number is used as first divisor. In this case with decimal numbers, the bars for integer part and decimal part are placed differently.
Real Life Question:
How are the lengths of diagonals of a room measured?
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Square root | A number which when multiplied by itself will form a square number. |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| Abacus | Represent the first divisor on the extreme left of the abacus. Leave enough room and represent the dividend. Now divide and note the value. If it is 0, stop further process. If it isn’t zero, double the first divisor and multiply it with 10. Chose a number such that (10n+a)a would give the new dividend. |
Real life uses :
Construction, business transactions, computer games, animations
Practical examples around us
| Examples | Explainations |
|---|---|
| Overhead tanks | The area of the tank is measured by dividing the capacity of tank with its proposed height. We use square roots to determine sides or radius |
| Computer games | The squares and square roots are used in construction of computer games during interactions of characters with objects |
What you learn in Theory:
Like subtraction and division, the inverse operations of addition and multiplication, finding a square root is the inverse operation of squaring a number. The bars are put on the integer part from units place to the left while in decimal part, they start from the point to the right. The first divisor is doubled and multiplied with 10 and then added with an expected number a such that the 10n+a will be the new divisor and a be the new digit in the quotient. The square root thus will be b.a.
What you learn in Practice:
The beads on the abacus result a new dividend after first division until the remainder of the previous operation is zero. When the remainder becomes 0, the noted down values of second division quotient is divided by ten and added with the quotient of the first step to get the square root.