Square Roots Grade 9 Important Language Perfect Squares

Square Roots Grade 9

Important Language Perfect Squares Square Roots of n-th order Fractional Powers Non-Perfect Radicals Pythagoras’ Theorem The following terms are going to be seen throughout this topic. Copy the words in your notebooks being sure to get to correct spelling… you never know when there will be a spelling quiz! Square Root Perfect Cube Root Perfect Square Surd Radicand Fractional Benchmark Order Hypotenuse

Perfect Squares Important Language Perfect Squares Square Roots of n-th order Fractional Powers Non-Perfect Radicals Pythagoras’ Theorem A perfect square is any fraction that can be written as the product of two equal fractions.

Perfect Squares Important Language Perfect Squares Square Roots of n-th order Fractional Powers Non-Perfect Radicals Pythagoras’ Theorem When thinking about perfect squares it could help to picture it in the following way:

Perfect Squares Important Language Perfect Squares Square Roots of n-th order Fractional Powers Non-Perfect Radicals Pythagoras’ Theorem In the past, we have only looked at perfect squares as whole numbers that are created by multiplying a different whole number by itself. Perfect squares can be a result of squaring a fraction, or a decimal. Write down a list of 10 fractional or decimal perfect squares and the numbers you multiply together to get them.

Square Roots Important Language Perfect Squares Square Roots of n-th order Fractional Powers Non-Perfect Radicals Pythagoras’ Theorem When we square root a perfect square we are trying to find what number was multiplied to get that perfect square. Example:

Square Roots Important Language Perfect Squares Square Roots of n-th order Fractional Powers Non-Perfect Radicals Pythagoras’ Theorem When calculating square roots that are more complex, try factor trees or long division Example:

Practice Important Language Perfect Squares Square Roots of n-th order Fractional Powers Non-Perfect Radicals Pythagoras’ Theorem

Square Root Laws Important Language Perfect Squares Square Roots of n-th order Fractional Powers Non-Perfect Radicals Pythagoras’ Theorem Just like with powers, there are rules that apply to using roots. Multiplication Law This law allows us to simplify surds

Simplifying Square Roots Important Language Perfect Squares Square Roots of n-th order Fractional Powers Non-Perfect Radicals Pythagoras’ Theorem Sometimes we are given surds that do not give whole number answers. In this case, we want to simplify the number under the root sign. Steps to solving: 1. Determine if the number under the square root sign is a product of a perfect square and another number 2. Write the product as two separate square roots 3. Evaluate the perfect square. Example:

Quick Questions

Square Root Laws Important Language Perfect Squares Square Roots of n-th order Fractional Powers Non-Perfect Radicals Pythagoras’ Theorem •

Practice Important Language Perfect Squares Square Roots of n-th order Fractional Powers Non-Perfect Radicals Pythagoras’ Theorem

Cube Roots Important Language Perfect Squares Square Roots of n-th order Fractional Powers Non-Perfect Radicals Pythagoras’ Theorem The same principals apply when finding roots that are not square roots. When finding a cube root, we are trying to figure out what number multiplies by itself three times in order to get that number Example:

Cube Roots Practice Important Language Perfect Squares Square Roots of n-th order Non-Perfect Radicals Pythagoras’ Theorem

Important Language Perfect Squares Square Roots of n-th order Fractional Powers Non-Perfect Radicals Pythagoras’ Theorem Fractional Indices and Radicals Roots can be written as exponents. This way we can use our power laws that we already know. Example: Surds can also be represented as having fractional exponents because, when converted, their power is a fraction.

Fractional Indices and Surds Important Language Perfect Squares Square Roots of n-th order Fractional Powers Non-Perfect Radicals Pythagoras’ Theorem Therefore, we can say that This applies to any root

Fractional Indices and Surds Important Language Perfect Squares Square Roots of n-th order Fractional Powers Non-Perfect Radicals Pythagoras’ Theorem Earlier, I mentioned that taking the square root of a perfect square will cancel out both the square root symbol and the power of two. Using your exponent laws, prove that

Important Language Perfect Squares Square Roots of n-th order Fractional Powers Non-Perfect Radicals Pythagoras’ Theorem Estimating Non-Perfect Radicals We need to know how to get a rough estimate of the value of a radical that has a non-perfect radicand (number underneath the radical sign) In order to estimate we need to follow these steps: 1. Find the closest perfect squares, above and below, the radicand 2. The decimal approximation will be between the square roots of these two numbers 3. Estimate, to the nearest tenth, depending on which number it is closer to.

Estimating Non-Perfect Radicals Important Language Perfect Squares Square Roots of n-th order Fractional Powers Non-Perfect Radicals Pythagoras’ Theorem

Estimating Non-Perfect Radicals Important Language Perfect Squares Square Roots of n-th order Fractional Powers Non-Perfect Radicals Pythagoras’ Theorem

Pythagoras’ Theorem Important Language Perfect Squares Square Roots of n-th order Fractional Powers Non-Perfect Radicals Pythagoras’ Theorem Remember this guy? ? He’s the one that said that the hypotenuse of a right-angled triangle is equal to the square root the square of the two opposite sides.

Pythagoras’ Theorem Important Language Perfect Squares Square Roots of n-th order Fractional Powers Non-Perfect Radicals Pythagoras’ Theorem works for every right-angled triangle. Remember that the hypotenuse is the longest side and is opposite to the right angle.

Pythagoras’ Theorem Important Language Perfect Squares Square Roots of n-th order Fractional Powers Non-Perfect Radicals Pythagoras’ Theorem Find the length of the hypotenuse