Step 1 x3−1x3 Take out the LCD:x3 →x3×x3x3−1x3 Make their denominators same →(x3×x3)−1x3 x3×x3=x×x3=x23=x23 ⇒=x23−1x3

Step 1 Look at these alternative ways of writing roots x is the same as x12 x3 is the same as x13 x4 is the same as x14 So for any number n xn is the same as x1n Step 2 Just picking a number at random I chose 3 Another way (not normally done) of writing 3 is 31 When you have 3×3 it can be written as 32 In the same way 3×3×3 can be written as 33 In the same way 3×3×3×3 can be written as 34 Notice that 3×3=31×31=31+1=32 Notice that 3×3×3=31×31×31=3(1+1+1)=33 Step 3 Given that a way of writing square root of 3 is 3 is 312 Compare what happens in each of the following two rows 31×31×31=31+1+1=33 312×312×312=312+12+12=332 Step 4 You asked about x3x3=x23 From above we know that x3 is the same as x13 But we have x3x3 This is the same as x13×x13=x13+13=x23 Step 5 Backtrack for a moment and again think about x13×x13 Like in 3×3=32 x13×x13=(x13)2 and x13×x13=x13+13=x23 Then (x13)2=x1×23=x23 Turning this back the other way x23=x23 Practise and a lot of it will fix this in your mind.

Step 1 x3−1x3 Take out the LCD:x3 →x3×x3x3−1x3 Make their denominators same →(x3×x3)−1x3 x3×x3=x×x3=x23=x23 ⇒=x23−1x3

Step 1 Look at these alternative ways of writing roots x is the same as x12 x3 is the same as x13 x4 is the same as x14 So for any number n xn is the same as x1n Step 2 Just picking a number at random I chose 3 Another way (not normally done) of writing 3 is 31 When you have 3×3 it can be written as 32 In the same way 3×3×3 can be written as 33 In the same way 3×3×3×3 can be written as 34 Notice that 3×3=31×31=31+1=32 Notice that 3×3×3=31×31×31=3(1+1+1)=33 Step 3 Given that a way of writing square root of 3 is 3 is 312 Compare what happens in each of the following two rows 31×31×31=31+1+1=33 312×312×312=312+12+12=332 Step 4 You asked about x3x3=x23 From above we know that x3 is the same as x13 But we have x3x3 This is the same as x13×x13=x13+13=x23 Step 5 Backtrack for a moment and again think about x13×x13 Like in 3×3=32 x13×x13=(x13)2 and x13×x13=x13+13=x23 Then (x13)2=x1×23=x23 Turning this back the other way x23=x23 Practise and a lot of it will fix this in your mind.

Solved: "What is x3−1x3?"

High School
Algebra
Pre-Algebra
Equations, expressions, and inequalitie

Seelakant6vr

Answered question

2022-02-02

What is

\sqrt[3]{x} - \frac{1}{\sqrt[3]{x}} ?

Answer & Explanation

Jaden Petersen

Beginner2022-02-03Added 15 answers

Step 1

\sqrt[3]{x} - \frac{1}{\sqrt[3]{x}}

Take out the

L C D : \sqrt[3]{x}

\to \frac{\sqrt[3]{x} \times \sqrt[3]{x}}{\sqrt[3]{x}} - \frac{1}{\sqrt[3]{x}}

Make their denominators same

\to \frac{(\sqrt[3]{x} \times \sqrt[3]{x}) - 1}{\sqrt[3]{x}}

\sqrt[3]{x} \times \sqrt[3]{x} = \sqrt[3]{x \times x} = \sqrt[3]{x^{2}} = x^{\frac{2}{3}}

\Rightarrow= \frac{x^{\frac{2}{3}} - 1}{\sqrt[3]{x}}

Amiya Wolf

Beginner2022-02-04Added 11 answers

Step 1 Look at these alternative ways of writing roots

\sqrt{x}

is the same as

x^{\frac{1}{2}}

\sqrt[3]{x}

is the same as

x^{\frac{1}{3}}

\sqrt[4]{x}

is the same as

x^{\frac{1}{4}}

So for any number n

\sqrt[n]{x}

is the same as

x^{\frac{1}{n}}

Step 2 Just picking a number at random I chose 3 Another way (not normally done) of writing 3 is

3^{1}

When you have

3 \times 3

it can be written as

3^{2}

In the same way

3 \times 3 \times 3

can be written as

3^{3}

In the same way

3 \times 3 \times 3 \times 3

can be written as

3^{4}

Notice that

3 \times 3 = 3^{1} \times 3^{1} = 3^{1 + 1} = 3^{2}

Notice that

3 \times 3 \times 3 = 3^{1} \times 3^{1} \times 3^{1} = 3^{(} 1 + 1 + 1) = 3^{3}

Step 3 Given that a way of writing square root of 3 is

\sqrt{3}

3^{\frac{1}{2}}

Compare what happens in each of the following two rows

3^{1} \times 3^{1} \times 3^{1} = 3^{1 + 1 + 1} = 3^{3}

3^{\frac{1}{2}} \times 3^{\frac{1}{2}} \times 3^{\frac{1}{2}} = 3^{\frac{1}{2} + \frac{1}{2} + \frac{1}{2}} = 3^{\frac{3}{2}}

Step 4 You asked about

\sqrt[3]{x} \sqrt[3]{x} = x^{\frac{2}{3}}

From above we know that

\sqrt[3]{x}

is the same as

x^{\frac{1}{3}}

But we have

\sqrt[3]{x} \sqrt[3]{x}

This is the same as

x^{\frac{1}{3}} \times x^{\frac{1}{3}} = x^{\frac{1}{3} + \frac{1}{3}} = x^{\frac{2}{3}}

Step 5 Backtrack for a moment and again think about

x^{\frac{1}{3}} \times x^{\frac{1}{3}}

Like in

3 \times 3 = 3^{2}

x^{\frac{1}{3}} \times x^{\frac{1}{3}} = (x^{\frac{1}{3}})^{2}

and

x^{\frac{1}{3}} \times x^{\frac{1}{3}} = x^{\frac{1}{3} + \frac{1}{3}} = x^{\frac{2}{3}}

Then

(x^{\frac{1}{3}})^{2} = x^{\frac{1 \times 2}{3}} = x^{\frac{2}{3}}

Turning this back the other way

x^{\frac{2}{3}} = \sqrt[3]{x^{2}}

Practise and a lot of it will fix this in your mind.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Pre-Algebra

Didn't find what you were looking for?