Calculating Squares and Square Root

A power in which the exponent is 2 is called a square

The square of the number can be calculated by multiplying the number by itself

a² = a x a

To solve an expression which contains squares, evaluate the squares first

Follow the standard order of operations and solve

a² = a x a

We can draw a grid of squares to check if a number is a perfect square

The number of squares that make up one side of the grid is the square root

To find the square root of a perfect square, think of a number, which when multiplied by itself, gives the square

If a x a = a², then √a² = a

A square root is denoted by the symbol ‘√’ (Square root of a is written √a)

We can use the square roots of perfect squares to help estimate the square roots of other numbers

Find the perfect squares close to the number.
For example: 40 is between the perfect squares 36 and 49

If a is between b and c, √a is between √b and √c. Find √b and √c

The best estimate of √a to the nearest whole number is the square root of the number which a is closer to.
For example: Best estimate of √40 to the nearest whole number is 6, since 40 is closer to 36 (6²) than 49 (7²)

If a < x < b, then –a > -x > -b

A number must be written in decimal form to check whether it’s rational or irrational

A decimal which is terminating is a rational number

A decimal which is non terminating is a rational number if it shows a repeating pattern

A non – terminating, non – repeating number is irrational

On a number line, numbers from left to right are in order from least to greatest