RD Sharma Class 8 Solutions Chapter 3 - Square and Square Roots (Ex 3.3) Exercise 3.3 - Free PDF
FAQs on RD Sharma Class 8 Solutions Chapter 3 - Square and Square Roots (Ex 3.3) Exercise 3.3
1. What is the core method taught in RD Sharma Class 8 Solutions for Exercise 3.3?
The primary method detailed in the solutions for Exercise 3.3 is the long division method for finding the square root of numbers. This includes finding the square roots of perfect squares, non-perfect squares, and decimal numbers, providing a step-by-step approach for each problem type.
2. How do you correctly pair digits before starting the long division method for a whole number like 53361?
To correctly pair the digits, you must start from the unit's place (the rightmost digit) and move left. Group the digits into pairs. For 53361, the pairs would be (61), (33), and the last digit (5) remains as a single bar. The division process starts with the leftmost bar, which is '5' in this case.
3. How does the long division method help find the square root of decimal numbers as per Chapter 3?
For decimal numbers, the pairing rule is slightly different:
- The integer part is paired from right to left.
- The decimal part is paired from left to right.
4. What is the step-by-step process for finding the least number that must be subtracted from a given number to get a perfect square?
To find the least number to be subtracted, follow these steps:
- Use the long division method to find the square root of the given number.
- The process will leave a remainder at the end because the number is not a perfect square.
- This remainder is the least number that must be subtracted from the original number to make it a perfect square. The quotient obtained is the square root of the new number.
5. Why is the new divisor doubled and a new digit added at each step in the long division method?
This step is based on the algebraic identity (a + b)² = a² + 2ab + b² = a² + (2a + b)b. At each stage, 'a' is the quotient found so far. The new divisor (2a + b) and the new digit in the quotient 'b' are chosen so that their product is less than or equal to the new dividend. Doubling the quotient ('2a') is a crucial part of constructing this new divisor.
6. When is the long division method more effective than using prime factorisation to find a square root?
The long division method is more effective in two main scenarios:
- When dealing with large numbers for which finding prime factors is very difficult and time-consuming.
- When finding the square root of numbers that are not perfect squares or for finding the value of a square root up to a certain number of decimal places. Prime factorisation only works for perfect squares.
7. How can you use the methods from RD Sharma Ex 3.3 to find the side of a square if its area is given as a decimal, for instance, 24.01 sq. units?
The side of a square is the square root of its area. To find the side when the area is 24.01, you need to calculate the square root of 24.01 using the long division method for decimals. By correctly pairing the digits as (24) and (01) and placing the decimal in the quotient, you can find the exact square root, which will be the length of the side of the square.
8. What is a common mistake to avoid when bringing down digits in the long division method for square roots?
A common mistake is bringing down only a single digit at a time, like in regular division. In the long division method for square roots, you must always bring down digits in pairs. The entire next bar (pair of digits) is brought down to form the new dividend. Forgetting this rule will lead to an incorrect answer.
