Question

What is 12 radical 2 divided by 2 radical 6 in simplest form

Answer 1

`=2√(3)\\\mathrm{Decimal:\quad }\:3.46410`

Explanation:

`(12√(2))/(2√(6))\\\mathrm{Divide\:the\:numbers:}\:(12)/(2)=6\\=(6√(2))/(√(6))\\\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a}=a^{(1)/(n)}\\√(6)=6^{(1)/(2)}\\=\frac{6√(2)}{6^{(1)/(2)}}\\\mathrm{Apply\:exponent\:rule}:\quad (x^a)/(x^b)=x^(a-b)\\\frac{6^1}{6^{(1)/(2)}}=6^{1-(1)/(2)}\\=√(2)\cdot \:6^{-(1)/(2)+1}\\\mathrm{Subtract\:the\:numbers:}\:1-(1)/(2)=(1)/(2)\\=6^{(1)/(2)}√(2)`

`\mathrm{Apply\:radical\:rule}:\quad \:a^{(1)/(n)}=\sqrt[n]{a}\\6^{(1)/(2)}=√(6)\\=√(6)√(2)\\\mathrm{Factor\:integer\:}6=2\cdot \:3\\=√(2\cdot \:3)√(2)\\\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}\\√(2\cdot \:3)=√(2)√(3)\\=√(2)√(3)√(2)\\\mathrm{Apply\:radical\:rule}:\quad √(a)√(a)=a\\√(2)√(2)=2\\=2√(3)`

Answer 2

`2 √(3)`

Explanation:

`( 12√(2) )/(2 √(6) )`

Reduce the fraction with 2

`= (6 √(2) )/( √(6) )`

Simplify the expression

`(6)/( √(3) )`

Multiply the fraction by
`( √(3) )/( √(3) )`

`(6)/( √(3) ) * ( √(3) )/( √(3) )`

To multiply the fractions, multiply the numerators and denominators separately

`\frac{6 √(3) }{ \sqrt{3 * √(3) } }`

When a square root of an expression is multiplied by itself, the result is that expression

`(6 √(3) )/(3)`

Reduce the fraction with 3

`2 √(3)`

Hope this helps...

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