Outro W13
Revie of the week
You can find the key concepts you studied this week in the following short reviews
9.4 Multiply Square Roots
- Product Property of Square Roots If a, b are nonnegative real numbers, then
\(\sqrt{ab}=\sqrt{a}\sqrt{b}\) and
\(\sqrt{a}\cdot\sqrt{b}=\sqrt{ab}\)
- Special formulas for multiplying binomials and conjugates:
\(\left(a+b\right)^2=a^2+2ab+b^2\)
\(\left(a-b\right)^2=a^2-2ab+b^2\)
\(a^2-b^2=\left(a-b\right)\left(a+b\right)\)
- The FOIL method can be used to multiply binomials containing radicals.
9.5 Divide Square Roots
- Quotient Property of Square Roots
- If a, b are non-negative real numbers and b≠0, then
\(\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}\) and
\(\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}}\)
- If a, b are non-negative real numbers and b≠0, then
- Simplified Square Roots
A square root is considered simplified if there are- no perfect square factors in the radicand
- no fractions in the radicand
- no square roots in the denominator of a fraction
9.6 Solve Equations with Square Roots
- To Solve a Radical Equation:
- Step 1. Isolate the radical on one side of the equation.
- Step 2. Square both sides of the equation.
- Step 3. Solve the new equation.
- Step 4. Check the answer. Some solutions obtained may not work in the original equation.
- Solving Applications with Formulas
- Step 1. Read the problem and make sure all the words and ideas are understood. When appropriate, draw a figure and label it with the given information.
- Step 2. Identify what we are looking for.
- Step 3. Name what we are looking for by choosing a variable to represent it.
- Step 4. Translate into an equation by writing the appropriate formula or model for the situation. Substitute in the given information.
- Step 5. Solve the equation using good algebra techniques.
- Step 6. Check the answer in the problem and make sure it makes sense.
- Step 7. Answer the question with a complete sentence.
- Area of a Square
- Falling Objects
- On Earth, if an object is dropped from a height of h feet, the time in seconds it will take to reach the ground is found by using the formula
t=√h4
- On Earth, if an object is dropped from a height of h feet, the time in seconds it will take to reach the ground is found by using the formula
- Skid Marks and Speed of a Car
- If the length of the skid marks is d feet, then the speed, s, of the car before the brakes were applied can be found by using the formula
s=√24d
- If the length of the skid marks is d feet, then the speed, s, of the car before the brakes were applied can be found by using the formula
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