Algebra Class 10 - Quadratic Equations

In simplification problems, you can often approximate numbers to make calculations easier. For example, 18 can be rounded to 20, and 26 can be rounded to 25. This makes the multiplication easier without significantly affecting the final answer.

To find the cube root of a number, you need to find the number that when multiplied by itself three times, equals the original number. For example, the cube root of 531441 is 81, because 81 x 81 x 81 = 531441.

A percentage is a way of representing a part of a whole as a fraction of 100. For example, 40% of 360 can be calculated as (40/100) x 360 = 144.

Fractions represent a part of a whole. To calculate a fraction of a number, you need to multiply the fraction by the number. For example, (2/17) of 14365 can be calculated as (2/17) x 14365.

When dealing with various arithmetic operations in simplification, it's important to follow the order of operations PEMDAS/BODMAS which stands for Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Square roots are numbers that when multiplied by themselves equal the original number. For example, the square root of 169 is 13, because 13 x 13 = 169.

The square root of a number can also be represented as its exponent to the power of 1/2. For example, √169 = 169^1/2 = 13.

In simplification problems, look for ways to simplify calculations by using common factors or grouping numbers. For example, 18 x 26 + 33² + 18² can be simplified by first calculating the squares of 33 and 18, then performing the multiplication and finally adding all the results.

The percentage profit is the difference between the selling price (SP) and the cost price (CP) expressed as a percentage of the CP. To calculate the profit percentage, use the formula: (SP - CP) / CP X 100.

To calculate the selling price (SP) after a certain percentage loss, multiply the original SP by (100% - loss percentage). For instance, if a product is sold at a 10% loss, the SP would be 90% of the original price.

The efficiency of someone or something is the rate at which work is completed. It represents the total units of work done in a given time. In this context, it refers to the combined work rate of multiple individuals.

The speed of a stream is the rate at which the water flows. It affects the speed of a boat traveling against or with the current. To find the speed of the stream, subtract the speed of the boat against the current from its speed with the current and divide by 2.

Quadratic equations are equations that contain a variable raised to the power of 2. To solve them, you need to find the values of the variable that make the equation true. There are different methods to solve quadratic equations, including factoring, completing the square, and using the quadratic formula.

The square root of a number is a value that, when multiplied by itself, equals the original number. For instance, the square root of 169 is 13, because 13 x 13 = 169.

The cube root of a number is the value that, when multiplied by itself three times, gives the original number. For example, the cube root of 531441 is 81, as 81 x 81 x 81 = 531441.

A percentage represents a part of a whole, expressed as a fraction of 100. For example, 40% of 360 means 40/100 x 360 = 144.

Fractions represent a part of a whole. To calculate a fraction of a number, multiply the fraction by that number. For instance, (2/17) of 14365 is (2/17) x 14365.

When dealing with a series of mathematical operations, it's important to follow the order specified by PEMDAS/BODMAS, ensuring a consistent approach to simplify any complex expression.

When you're solving a mathematical problem, you can often estimate the answer by rounding numbers to make the calculations easier. This helps to find a close approximation without working with exact figures.

Finding the incorrect number in a sequence by identifying the pattern.

In this type of series, each number is obtained by multiplying the preceding number with a constant and then adding a constant.

In this type of series, each number is obtained by adding a constant to the product of the preceding number with a constant.

In this type of series, each number is obtained by the sum of the previous two numbers.

In this type of series, each number is obtained by subtracting a constant from the product of the preceding number with a constant.

In this type of series, each number is obtained by dividing the preceding number by a constant and then adding a constant.

In this type of series, each number is obtained by adding a constant to the quotient of the preceding number by a constant.

In this type of series, each number is obtained by subtracting a constant from the quotient of the preceding number by a constant.

In this type of series, each number is obtained by adding a constant to the difference of the preceding number by a constant.

In this type of series, each number is obtained by subtracting a constant from the difference of the preceding number by a constant.