Seelakant6vr

2022-02-02

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

Jaden Petersen

Beginner2022-02-03Added 15 answers

Step 1
$\sqrt[3]{x}-\frac{1}{\sqrt[3]{x}}$
Take out the $LCD:\sqrt[3]{x}$
$\to \frac{\sqrt[3]{x}\times \sqrt[3]{x}}{\sqrt[3]{x}}-\frac{1}{\sqrt[3]{x}}$
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 $\sqrt{3}$ is ${3}^{\frac{1}{2}}$
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.

Which expression has both 8 and n as factors???

One number is 2 more than 3 times another. Their sum is 22. Find the numbers

8, 14

5, 17

2, 20

4, 18

10, 12Perform the indicated operation and simplify the result. Leave your answer in factored form

$\left[\frac{(4x-8)}{(-3x)}\right].\left[\frac{12}{(12-6x)}\right]$ An ordered pair set is referred to as a ___?

Please, can u convert 3.16 (6 repeating) to fraction.

Write an algebraic expression for the statement '6 less than the quotient of x divided by 3 equals 2'.

A) $6-\frac{x}{3}=2$

B) $\frac{x}{3}-6=2$

C) 3x−6=2

D) $\frac{3}{x}-6=2$Find: $2.48\xf74$.

Multiplication $999\times 999$ equals.

Solve: (128÷32)÷(−4)=

A) -1

B) 2

C) -4

D) -3What is $0.78888.....$ converted into a fraction? $\left(0.7\overline{8}\right)$

The mixed fraction representation of 7/3 is...

How to write the algebraic expression given: the quotient of 5 plus d and 12 minus w?

Express 200+30+5+4100+71000 as a decimal number and find its hundredths digit.

A)235.47,7

B)235.047,4

C)235.47,4

D)234.057,7Find four equivalent fractions of the given fraction:$\frac{6}{12}$

How to find the greatest common factor of $80{x}^{3},30y{x}^{2}$?