Question

Simplify the square root of 2 multiplied by the cube root of 2
how do i work this out @texaschic101

Answer 1

@sheelo_mughal @phi @aaronq @waterineyes @johnweldon1993

Answer 2

\[\large \sqrt{2} \times \sqrt[3]{2} = (2)^{\frac{1}{2}} \times (2)^{\frac{1}{3}}\]

Answer 3

\[\large \sqrt{2} \sqrt[3]{2}\]

Remember that we can write this as

\[\large 2^{1/2} 2^{1/3}\]

And when we multiply this...we just add the exponents

\[\large 1/2 + 1/3 = 5/6\]

so we have

\[\large 2^{5/6}\]

Answer 4

And you can here use the indices rule that:

\[(x)^a \times (x)^b = (x)^{a+b}\]

Answer 5

Getting @jadee27p ??

Answer 6

yes still confused though

Answer 7

about the 1/2

Answer 8

Square root means 1/2

Like cube root means 1/3

Generally we must represent sqrt(2) as:

\[\huge \sqrt[2]{2}\]

Answer 9

But these square root brackets tell you that you are doing square root only, so we don't write 2 in front of the brackets..

But for 3, 4, 5th roots, you have to write in front..

Answer 10

Like cube root you will write as:

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

Fourth root you will write as:

\[\sqrt[4]{x}\]

But square root can be written as :

\[Either \quad \sqrt{x} \quad or \quad \sqrt[2]{x}\]

Answer 11

Getting till here??

Answer 12

Right, just remember the rule

\[\Large \sqrt[b]{a^c} = a^{c/b}\]

so

\[\Large \sqrt[2]{2^1} = 2^{1/2}]\]
and
\[\Large \sqrt[3]{2^1} = 2^{1/3}\]

Answer 13

Look for this one:

For \(\sqrt[m]{x}\), you can write it as : \((x)^{\frac{1}{m}}\)..