Square roots of perfect squares | Square roots and cube roots. Understanding square roots | Square roots and cube roots. Square roots of perfect squares. Squares and square roots. Squares and Square Roots. The square of a number? When we multiply an integer by itself we call the product the square of the number. For example: 4 x 4 = 16 The square of 4 is 16 The pictures above show why we call these products squares. Squared Numbers The examples below show how squares can be found. Squared Words! You'll hear different words used when people talk about squares. e.g. Square of a number: 25 is the square of 5 Squaring a number: multiplying the number by itself A squared number: 100 is a square number 3 squared: 3 squared is 9 What's the square of 9?
Make sure your children know the short way of finding a square on a calculator. e.g. to find 6 x 6, enter 6, x, = Writing squares Squares are powers of two. We write squares using the same notation that we use with other powers. We could talk about 3 to the power of 2, or the second power of three but we don't usually do so; we say 3 squared. Square Roots You can think of finding square roots as the opposite of finding squares. Writing Square Roots. Powers: Bases and Exponents.
Powers and exponents. We know how to calculate the expression 5 x 5. This expression can be written in a shorter way using something called exponents. An expression that represents repeated multiplication of the same factor is called a power. The number 5 is called the base, and the number 2 is called the exponent. The exponent corresponds to the number of times the base is used as a factor. Example: Write these multiplications like exponents Multiplication: If two powers have the same base then we can multiply the powers.
The rule: Division: If two powers have the same base then we can divide the powers. A negative exponent is the same as the reciprocal of the positive exponent. When you raise a product to a power you raise each factor with a power The rule for the power of a power and the power of a product can be combined into the following rule: Video lesson: Rewrite the expressions Video lesson: Simplify the expression. Exponents. The exponent of a number says how many times to use the number in a multiplication. In 82 the "2" says to use 8 twice in a multiplication, so 82 = 8 × 8 = 64 In words: 82 could be called "8 to the power 2" or "8 to the second power", or simply "8 squared" Exponents are also called Powers or Indices.
Some more examples: Example: 53 = 5 × 5 × 5 = 125 In words: 53 could be called "5 to the third power", "5 to the power 3" or simply "5 cubed" Example: 24 = 2 × 2 × 2 × 2 = 16 In words: 24 could be called "2 to the fourth power" or "2 to the power 4" or simply "2 to the 4th" Exponents make it easier to write and use many multiplications Example: 96 is easier to write and read than 9 × 9 × 9 × 9 × 9 × 9 You can multiply any number by itself as many times as you want using exponents.
Try here: In General So in general: Other Way of Writing It Sometimes people use the ^ symbol (just above the 6 on your keyboard), as it is easy to type. Example: 2^4 is the same as 24 Negative Exponents Negative? Dividing! Square Roots. Squares and Square Roots. First learn about Squares, then Square Roots are easy. How to Square A Number To square a number, just multiply it by itself ... Example: What is 3 squared? "Squared" is often written as a little 2 like this: This says "4 Squared equals 16" (the little 2 says the number appears twice in multiplying) Squares From 12 to 62 Negative Numbers We can also square negative numbers. That was interesting! When we square a negative number we get a positive result. Just the same as if we had squared a positive number: (For more detail read Squares and Square Roots in Algebra) Note: if someone says "minus 5 squared" do we: Square the 5, then do the minus?
We get different answers: Always make it clear what you mean, and that is what the "( )" are for. Square Roots A square root goes the other way: 3 squared is 9, so a square root of 9 is 3 A square root of a number is ... ... a value that can be multiplied by itself to give the original number. A square root of 9 is ... It is like asking: Decimal Numbers So the answer is: