List of Important Square Root Numbers for Students
The square root of numbers is an important mathematical concept that should be clear to students. Learning square roots and squares of a number will increase a student’s interest and understanding of how mathematical concepts work. Learning squares and square roots of all the numbers is an impossible task. However, students should at least know these values up to 50. By memorising squares and square roots of numbers from 1 to 50, students will be able to attempt their question papers quickly.
This will not only increase your speed while calculating but also give you more time to attempt more complex questions. While attempting your question paper, it is important to plan your paper. You want your calculations to be fast but also accurate at the same time. The more you practice these numbers, the more they will become engraved to your memory.
Square Roots List
Square roots 1 to 50 list is given below. Students can use this list to memorise the values of squares and square roots of numbers from 1 to 50. To learn values above 50 is a difficult task but not impossible. Learning all the values at once can be a daunting task. So it is advised to learn them in groups. It is also important to put them to use when you are practising to memorise the values.
Square Root Numbers List
Every positive number can have a positive and a negative root. The is called the radical sign and is used to depict the square root of any number.
√4 =2
As, 2 x 2 = 4
Also (-2) x (-2) = 4
Therefore, 4 has 2 square roots, 2 and -2
Square roots of negative numbers are studied under the concepts of complex numbers. Also squaring can be talked about in other mathematical concepts. To square two matrices is to multiply them with each other. The meaning of squaring or square root remains the same.
FAQs on Square Root Numbers Explained
1. What is a perfect square and can you list the perfect squares between 1 and 100?
A perfect square is a number that is the product of an integer with itself. In other words, its square root is a whole number with no decimal part. For students, memorising these helps in faster calculations. The perfect squares from 1 to 100 are: 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100.
2. What is the relationship between the square and the square root of a number?
Squaring and finding the square root are inverse operations. This means they undo each other. For example, if you take the number 8 and square it, you get 64 (8 x 8 = 64). If you then find the square root of 64 (√64), you get back to the original number, 8. This complementary relationship is fundamental to solving many algebraic equations.
3. How can you simplify the square root of a non-perfect square like √1250?
You can simplify the square root of a non-perfect square using the prime factorisation method. First, break down the number into its prime factors: 1250 = 2 × 5 × 5 × 5 × 5. Next, group the identical factors into pairs: 1250 = 2 × (5 × 5) × (5 × 5). For each pair of factors, you can take one factor out of the square root sign. This gives you 5 × 5 × √2, which simplifies to 25√2.
4. What are the two main methods to find the square root of a number as per the CBSE syllabus?
The two primary methods taught in the CBSE curriculum for finding square roots are:
- Prime Factorisation Method: This method is ideal for perfect squares. It involves finding all the prime factors of a number and then grouping them into identical pairs. The product of one factor from each pair gives the square root.
- Long Division Method: This is a versatile, step-by-step method used for large numbers and non-perfect squares. It is also the standard method for finding the square root of decimal numbers to a required precision.
5. How do you find the square root of a decimal number, for instance, 12.25?
To find the square root of a decimal number like 12.25, you use the long division method. Start by pairing the digits, beginning from the decimal point. The integer part (12) is one pair, and the decimal part (25) is another. Place the decimal point in the quotient directly above the decimal point in the number. Then, proceed with the division process as you would for a whole number. The square root of 12.25 is 3.5.
6. How can you quickly tell if a number cannot be a perfect square just by looking at it?
You can quickly identify that a number is not a perfect square by checking its last digit (the digit in the unit's place). A number that ends with 2, 3, 7, or 8 can never be a perfect square. This property serves as a quick check to eliminate options in problems without needing to perform complex calculations.
7. Why is understanding square roots important for topics outside of this chapter?
Understanding square roots is crucial because it is a foundational concept for many advanced topics in mathematics and science. For example:
- In Geometry, it is used extensively in the Pythagoras theorem to find the length of sides in a right-angled triangle.
- In Physics, various formulas for calculating distance, velocity, and time involve square roots.
- In Algebra, it is essential for solving quadratic equations.
8. Is the square root of a number always smaller than the number itself?
No, this is a common misconception. While this holds true for all numbers greater than 1 (e.g., √16 = 4, which is less than 16), the rule is different for numbers between 0 and 1. For these numbers, the square root is actually larger. For example, the square root of 0.25 is 0.5, which is greater than 0.25. For the numbers 0 and 1, the square root is equal to the number itself.
