Week 4-Precalc 11

yil2016 on September 29, 2018October 4, 2018

In this week, I learn how to add, subtract, multiply and divide radicals ,actually all of the radicals is similar to the way that expressions calculated. An expression is composed of coefficient, variables and terms. The calculate of expression you just need going to evaluate the coefficient of the expression, as the same way to do radical. Nonetheless simplifying the radical expressions have been done at the beginning makes calculation more easier.

Add: $\sqrt[n]{a}+3\sqrt[n]{a}=4\sqrt[n]{a}$ , (a≥0)

(1) Simplify radical expressions

(2) Group the radical expressions that have same radical,such as $\sqrt{2},2\sqrt{2},3\sqrt{2}$

(3) Calculate the coefficient have same radical only

EX: $\sqrt{36x}+\sqrt{16x}+\sqrt{4x}=6\sqrt{x}+4\sqrt{x}+2\sqrt{x}=12\sqrt{x}$ . (x≥0)

Subtract: $\sqrt[n]{a}-3\sqrt[n]{a}=-2\sqrt[n]{a}$ , (a≥0)

(1) Simplify radical expression

(2) Group the radical expressions that have same radical,such as $\sqrt{3},2\sqrt{3},3\sqrt{3}$

(3) Calculate coefficients have same radical only

EX: $\sqrt{8x}-\sqrt{32x}-\sqrt{27x}=2\sqrt{2x}-4\sqrt{2x}-3\sqrt{3x}=-2\sqrt{2x}-3\sqrt{3x}$ , (x≥0)

Multiply： $\sqrt[n]{a}\cdot\sqrt[n]{b}=\sqrt[n]{ab}$ , (a≥0 & b≥0)

The biggest difference between multiplication and addition and subtraction is not just multiplying coefficients, but also radicand.

(1) Simplify radical expression

(2) Calculate coefficients and radicals respectively

(3)Simplify the product

EX: $\sqrt{8x}(\sqrt{2x}-\sqrt{3x})=2\sqrt{2x}(\sqrt{2x}-\sqrt{3x})=2\sqrt{4x^2}-2\sqrt{6x^2}=4x-2x\sqrt{6}$ , (x≥0)

Divide: $\frac{a}{\sqrt{b}}=\frac{a}{\sqrt{b}}\cdot\frac{\sqrt{b}}{\sqrt{b}}=\frac{a\sqrt{b}}{b}$ , (b＞0)

(1) Simplify radical expression

(2) Calculate coefficients and radicals respectively

(3)Simplify the product

EX: $\frac{2}{\sqrt{3}}=\frac{2}{\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}}=\frac{2\sqrt{3}}{3}$

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